The fractions as 50/15 and 6/15, respectively, and subtract them to obtain w = 44/15. This can be further simplified to the mixed number 2 14/15 or the decimal approximation 2.933.
To solve the equation w + 2/5 = 3 1/3, we need to isolate w on one side of the equation by subtracting 2/5 from both sides, finding a common denominator, and simplifying the resulting expression to obtain w.
w + 2/5 = 10/3
To isolate w, we need to move the constant term on the right-hand side of the equation to the left-hand side by subtracting 2/5 from both sides.
Subtracting 2/5 from both sides:
w = 10/3 - 2/5
To add these fractions, we need to find a common denominator, which is 15. So we can rewrite the fractions as:
w = (50/15) - (6/15)
Combining like terms:
w = 44/15
Therefore, w = 2 14/15 or approximately 2.933.
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y = y₁ = m(x − x₁)
Show your work in the space provided below.
1. Find the equation of the line that has a slope of -4 and passes through the point (-3, 7).
Show your work below:
2. Find the equation of the line that passes through the points (4, -3) and (8,9).
Show your work below:
Answer:
see below
Step-by-step explanation:
The equation y - y₁ = m(x − x₁)
1. y - 7 = -4(x - -3)
y - 7 = -4(x + 3)
y = -4x - 12 + 7
y = -4x - 5
2. y - y₁ = m(x − x₁)
9 - -3 = m(8 - 4)
12 = 4m
m = 12/4 = 3
y = mx + b
-3 = 3(4) + b
b = - 3 - 12
b = -15
y = 3x - 15
Select the best answer for the question.
4
ol
0
-1 2
-3
-1
15. Multiply
0
A. -6
3
4
1
-4
0
-3 1
Answer:
40 -12-3 15 multiply all of them and u get your answer
Given vectors u = (2, 5) and v = (-5, -2), find the difference u - v and
represent the difference graphically in two different ways.
The difference between two vectors [tex](u - v )[/tex] = [tex](7,7)[/tex].
What is vectors?An entity with both magnitude and direction is referred to as a vector. A vector can be visualized geometrically as a directed line piece, with an arrow pointing in the direction and a length equal to the magnitude of the vector. The vector points in a direction from its tail to its head.
Therefore subtracting [tex]u-v[/tex] we get
[tex]u-v = (2,5)-(-5,-2\\ = (2+5,5+2)\\=(7,7)[/tex]
The distinction between u and v can be graphically represented in two ways:
The next step is to create the vector [tex]u-v[/tex], which begins at the same location as [tex]u[/tex] and ends at [tex]v[/tex].
In an algebraic sense, the vectors u and v can be represented as points in a coordinate plane, and the vector u - v as a line connecting these places.
The following figure shows the construction with negative velocities
In this case, the vectors u and v are represented by location A and point B, respectively.
Therefore the difference between two vectors [tex](u - v )[/tex] = [tex](7,7)[/tex].
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can someone help me do this (will give brainliest if possible
Answer:
4) ∠1 and ∠2, ∠2 and ∠3
5) ∠1 and ∠3
6) x = 10
Step-by-step explanation:
Adjacent angles are two angles that share a common vertex and a common side, but do not overlap.
Therefore, the pairs of adjacent angles in the given diagram are:
∠1 and ∠2∠2 and ∠3∠3 and ∠4∠4 and ∠5∠5 and ∠1Vertical angles are pairs of non-adjacent angles that are formed when two lines intersect. Vertical angles are congruent,
Therefore, the pair of vertical angles in the given diagram are:
∠1 and ∠3As ∠1 and ∠3 are the same measure:
⇒ m∠1 = m∠3
⇒ (9x)° = 90°
⇒ 9x = 90
⇒ 9x ÷ 9 = 90 ÷ 9
⇒ x = 10
Therefore, the value of x is 10.
Answer:
4) ∠1 and ∠2, ∠2 and ∠3.
5) ∠1 and ∠3.
6) x = 10.
Step-by-step explanation:
Explanations are given in attachment!
Andy has -$45 in his checking account at the beginning of the week. At the end of the week he was paid $30 for moving the grass and $25 for vacuuming the house. How much money does Andy now have in his checking account?
Answer:
we need to add the money Andy earned to the negative balance he had. So, we have:
-$45 + $30 + $25 = $10
Therefore, Andy now has $10 in his checking account.
Answer:
Andy now has $10 in his checking account.
Step-by-step explanation:
Andy starts the week with -$45 in his checking account. When he gets paid $30 for mowing the grass and $25 for vacuuming the house, his total earnings for the week are:
$30 + $25 = $55
To find out how much money he now has in his checking account, we need to add his earnings to his starting balance of -$45. Adding a negative number is the same as subtracting a positive number, so we can write this as:
-$45 + $55 = $10
Therefore, Andy now has $10 in his checking account.
Let x represent one number and let y represent the other number. Use the following conditions to write a system of nonlinear equations. Solve the system and find the numbers.
The sum of two numbers is 11 and the product of the two numbers is 30
The two numbers are:
(use a comma to separate answers as needed)
Answers:
There are 2 answers:
1. 6,5
2. 5,6
Step-by-step explanation:
The SUM of two numbers IS 11:
x + y = 11
The PRODUCT of two numbers IS 30:
xy = 30
The system we get is
x + y = 11
xy = 30
Now solve the system:
There are 2 possible solutions:
(6,5) and (5,6)
Twenty four blood samples were selected by taking every seventh blood sample from racks holding 199 blood samples from the morning draw at a medical center
A)calculate the FPCF for this sample
B)Should the population be considered effectively infinite
DO BOTH A AND B URGENT
A) The FPCF for this sample is 0.899. B) The sample size is about 12% of the population size, which is relatively large.
A) The FPCF (Finite Population Correction Factor) is used to adjust for the impact of a finite population on the sampling distribution. The formula for the FPCF is:
FPCF = [tex]\sqrt{((N-n)/(N-1))}[/tex]
where N: size of the population and n: size of the sample.
In this case, the population size is N = 199, and the sample size is n = 24. Therefore, the FPCF can be calculated as follows:
FPCF = [tex]\sqrt{((199-24)/(199-1))}[/tex] = 0.899
So, the FPCF for this sample is 0.899.
B) In general, a population can be considered effectively infinite when the sample size is no more than 5-10% of the population size. In this case, the sample size is n = 24, and the population size is N = 199. Therefore, the sample size is about 12% of the population size, which is relatively large.
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options.
NEED ASAP
Answer choices:
y(y + 5) = 750
y2 – 5y = 750
750 – y(y – 5) = 0
y(y – 5) + 750 = 0
(y + 25)(y – 30) = 0
The equations that can be used to solve for y in the given situation are:
(A) y(y + 5) = 750
(B) y² – 5y = 750
(D) y(y – 5) + 750 = 0
What is a rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°).
A rectangle has equal and parallel opposite sides.
A rectangle has two dimensions—length and width—because it is a two-dimensional form.
The rectangle's longer side is its length, while its shorter side is its breadth.
So, the area formula of the rectangle:
750 = l * w
750 = x * (x-5)
750 = x² - 5x
x² - 5x - 750 = 0
Equations in the options that are similar:
(A) y(y + 5) = 750
(B) y² – 5y = 750
(D) y(y – 5) + 750 = 0
Therefore, the equations that can be used to solve for y in the given situation are:
(A) y(y + 5) = 750
(B) y² – 5y = 750
(D) y(y – 5) + 750 = 0
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Correct question:
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options.
NEED ASAP
Answer choices:
a. y(y + 5) = 750
b. y2 – 5y = 750
c. 750 – y(y – 5) = 0
d. y(y – 5) + 750 = 0
e. (y + 25)(y – 30) = 0
complete the diagram
4 →6
2→___
___→ -3
Answer:
The missing values to complete the diagram are:
4 → 6
2 → 5
-1 → -3
To find the missing values, we need to follow the pattern of the given arrows.
Starting with 4 and going to 6, we add 2 to get to the next number. So, starting with 2, we add 3 to get the missing value of 5.
Going from 2 to 5, we add 3 once again. So, to get from 5 to the next number, we add 3 to get 8.
To find the missing value that goes from an unknown number to -3, we need to subtract 3. Since we have already used the numbers 2 and 4, we can try a negative number. Starting with -1 and subtracting 3 gives us the missing value of -3.
Therefore, the completed diagram would look like this:
4 → 6
2 → 5
-1 → -3
Another MethodHere's the completed diagram with the missing values filled in based on the pattern:
```
4 → 6
2 → 4
-1 → -3
```
The pattern seems to be that for each input value (x), the output value (y) is x + 2.
Help plsSSSSSSSSSSSSSSSSSSSSSSS
Step-by-step explanation:
[tex]\triangle ADB[/tex] is equilateral, so [tex]m\angle DBA=60^{\circ}[/tex].
Using linear pairs, [tex]m\angle DBC=120^{\circ}[/tex].
Answer: J (120)
Step-by-step explanation: Since triangle ABD is given to be an equalatiral triangle, we know that every interior angle is 60 degrees. Since line ABC is a straight line we know that if we subtract the lines angle (180) by the interior angle it goes through (60) we get the measure of angle DBC: 120 degrees
Simplify -4x(1-3)-2x+2)
Answer:
The answer is 6x + 2
Step-by-step explanation
I did all the work and I passed on this test so i know this is the answer.
The polynomial of degree 4, P(x) , has a root of multiplicity 2 at x=3 and a root of multiplicity 1 at x=0 and x=-1. it goes through point (5,12).
Triangle ABC is shown. Use the graph to answer the question. triangle ABC on a coordinate plane with vertices at 1 comma negative 2, 9 comma negative 2, 5 comma 2 Determine the coordinates of the image if triangle ABC is translated 5 units down. A′(−4, −2), B′(4, −2), C′(0, 2) A′(1, −7), B′(9, −7), C′(5, −3) A′(1, 3), B′(9, 3), C′(5, 7) A′(6, −2), B′(14, −2), C′(10, 2)
if triangle ABC is translated 5 units down, the image's coordinates are A′(1, 7), B′(9, 7), and C′(5, 3).
The x and y coordinates of each of a triangle's vertices must be added to or subtracted from to translate the triangle on a coordinate plane.
Triangle ABC must be translated five units lower in this situation. Thus, we must deduct 5 from the y coordinates of each of its vertices.
A(1, -2) changes to A' (1, -7) B(9, -2) changes to B' (9, -7) C(5, 2) changes to C' (5, -3)
As a result, if triangle ABC is translated 5 units down, the image's coordinates are A′(1, 7), B′(9, 7), and C′(5, 3).
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x^3-6x^+2x-4 divided by x+2
Answer:
Step-by-step explanation:
Nathan rolls a number cube and records the result of each roll in the table.
Number Cube
Number Rolled
Frequency
1
11
2
16
3
14
4
20
5
12
6
17
Which statements below represent the situation? Select three options.
The correct three options are:
Nathan rolled a number cube and recorded the results in a table.
The number cube has six sides, numbered 1 through 6.
The number 4 was rolled more frequently than any other number.
Nathan rolled a number cube and recorded the results in a table.
The number cube has six sides, numbered 1 through 6.
Nathan rolled the number cube a total of 90 times.
The number 4 was rolled more frequently than any other number.
The number 2 was rolled the least frequently of all the numbers.
The total number of rolls for odd numbers is greater than the total number of rolls for even numbers.
The correct statements are:
Nathan rolled a number cube and recorded the results in a table.
The number cube has six sides, numbered 1 through 6.
The number 4 was rolled more frequently than any other number.
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i literally don’t understand any of this
According to the information, he quadratic function's equation is f(x) = (47/13)x^2 + (89/13)x + 198/13 in standard form.
How to find the quadratic function's equation?To find the quadratic function's equation, we need to use the given points from the table and solve for the coefficients a, b, and c in the standard form of a quadratic function, f(x) = ax^2 + bx + c.
Using the point (-7, 209):
209 = a(-7)^2 + b(-7) + c
Using the point (-5, 113):
113 = a(-5)^2 + b(-5) + c
Using the point (-2, 29):
29 = a(-2)^2 + b(-2) + c
Now we have three equations with three variables. We can solve for a, b, and c using a system of linear equations. First, simplify each equation:
49a - 7b + c = 209
25a - 5b + c = 113
4a - 2b + c = 29
Then, we can solve for b in terms of a and substitute in the other equations to eliminate b:
b = 7a + c/7 - 29/7
Substituting into the second equation:
25a - 5(7a + c/7 - 29/7) + c = 113
Simplifying:
10a + c = 80
Substituting into the third equation:
4a - 2(7a + c/7 - 29/7) + c = 29
Simplifying:
-3a + c = 33
Now we have two equations with two variables. We can solve for c in terms of a and substitute back into one of the previous equations to solve for a:
c = 3a + 33
Substituting into the second equation:
10a + (3a + 33) = 80
Simplifying:
13a = 47
a = 47/13
Now we can substitute a back into one of the previous equations to solve for c:
c = 3(47/13) + 33 = 198/13
Finally, we can substitute a and c into the standard form of a quadratic function:
f(x) = (47/13)x^2 + (7(47/13) - 198/13)x + 198/13
Simplifying:
f(x) = (47/13)x^2 + (89/13)x + 198/13
Therefore, the quadratic function's equation is f(x) = (47/13)x^2 + (89/13)x + 198/13 in standard form.
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Write 4 as a logarithm with a base 4
Answer: Algebra Examples
Logarithm base 4 of 4 is 1.
Step-by-step explanation:
unity
The value of log 4 to the base 4 is equal to unity. The Antilogarithm of the logarithmic value of 4 is equal to 4.
I put a picture please help
Describe the transformation of LM to L'M'.
O A. LM is translated 5 units left and 2 units down to L'M':
O B. LM is translated 5 units right and 2 units up to L'M
O C. LM is reflected over the x-axis to L'M'.
O'D. LM is reflected over the y-axis to L'M
SUBMIT
The option that Describe the transformation of LM to L'M'. is: LM is translated 5 units left and 2 units down to L'M'. Answer: option A.
What is the transformation about?To determine the transformation from LM to L'M', we need to identify how much LM has been translated horizontally and vertically. From the graph, we can see that L has been moved 5 units to the left to reach L', and M has been moved 2 units down to reach M'.
Looking at the graph, we can see that L is moving leftward and downward, while M is moving leftward. This indicates a translation.
Furthermore, the distance that L and M move is 5 units horizontally and 2 units vertically. This means that LM is translated 5 units left and 2 units down to L'M'.
Therefore, the correct answer is OA. LM is translated 5 units left and 2 units down to L'M'.
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Suppose you want to save $7,500 to go on a dream vacation in three years. You can save for your vacation by either depositing one single lump of money into a savings account and letting it accumulate interest or by making regular monthly payments.
You would need to deposit approximately $8,267.40 initially to reach your goal of $7,500 in three years, assuming an annual interest rate of 3%.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
If you have three years to save for a dream vacation and want to save $7,500, there are two main approaches you can take: making regular monthly payments or depositing one single lump sum into a savings account.
Option 1: Regular Monthly Payments
If you decide to make regular monthly payments towards your vacation savings, you will need to calculate how much you need to save each month to reach your $7,500 goal. To do this, you need to divide the total amount you want to save by the number of months you have to save.
In this case, you have 36 months (3 years x 12 months/year) to save $7,500, so:
$7,500 ÷ 36 = $208.33 per month
So, you would need to save approximately $208.33 per month for 36 months to reach your goal of $7,500.
Option 2: Single Lump Sum Deposit
If you decide to deposit one single lump sum into a savings account, you will need to calculate how much you need to deposit initially to reach your $7,500 goal in three years, assuming a certain rate of interest.
The amount you need to deposit will depend on the interest rate you can earn on your savings. For example, if you can earn an annual interest rate of 3%, the calculation would be:
Initial deposit = Future value of $7,500 at 3% interest over 3 years
Using a financial calculator or spreadsheet, you can determine that the future value of $7,500 at 3% interest over 3 years is approximately $8,267.40.
Therefore, You would need to deposit approximately $8,267.40 initially to reach your goal of $7,500 in three years, assuming an annual interest rate of 3%.
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Question 2 (1 point)
What are the multiplicative and additive inverses of -7?
a
multiplicative inverse 1/7; additive inverse -7
b
multiplicative inverse 1/7; additive inverse 7
c
multiplicative inverse -1/7; additive inverse -7
d
multiplicative inverse -1/7; additive inverse 7
answer is option D ,The multiplicative inverse of a number is the reciprocal of that number such that when you multiply them together, you get one. The multiplicative inverse of -7 is -1/7.
what is multiplicative inverse ?
The multiplicative inverse of a number is also known as its reciprocal. It is the number that, when multiplied by the original number, results in a product of 1. In other words, if the original number is a, then its multiplicative inverse
In the given question,
The additive inverse of a number is the opposite of that number such that when you add them together, you get zero. The additive inverse of -7 is 7.
The multiplicative inverse of a number is the reciprocal of that number such that when you multiply them together, you get one. The multiplicative inverse of -7 is -1/7.
Therefore, the correct answer is (c) multiplicative inverse -1/7; additive inverse -7.
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Rachel cycled a total distance of 59,136ft on a bicycle path surrounding a lake. She cycled 4 laps, where each lap was the same length. What was the length of each lap around the lake? Write your answer in miles.
Rachel cycled each lap around the lake that was 2.8 miles long.
What is unit rate?
A unit rate is a ratio in which the denominator is 1. It is a rate that compares a quantity to one unit of another quantity.
First, we need to convert the total distance cycled from feet to miles since the length of each lap is likely to be expressed in miles.
1 mile = 5280 feet
Therefore,
59,136 ft ÷ 5280 ft/mile = 11.2 miles
So, Rachel cycled a total of 11.2 miles around the lake.
Since she cycled 4 laps of the same distance, we can divide the total distance by 4 to get the length of each lap:
11.2 miles ÷ 4 = 2.8 miles per lap
Therefore, Rachel cycled each lap around the lake that was 2.8 miles long.
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Which inequality is true?
A 0.23 < 0.089
B 1.035 > 1.04
© 2.358 < 2.369
D 99.863 > 99.901
Answer:
C
Step-by-step explanation:
We Can see from the < pointing to the higher side.
HELP I NEED THIS ASAPPP!!!
Mr. Harris graded papers at the end of the school day. The table below shows how many papers he graded in minutes.
Minutes Number of papers graded
4 2
16 8
20 10
24 12
At this rate, how many papers will Mr. Harris grade in 60 minutes?
30 papers
36 papers
48 papers
52 papers
The number of papers that will be graded in 60 minutes is 30 papers.
What is proportion?Proportion refers to the relationship or comparison between two or more quantities or values. It expresses how one quantity relates to another in terms of size, magnitude, or scale. Proportions are often used to describe the relative sizes or ratios of different elements within a whole or between different parts of a whole.
We have that;
2 papers are graded in 4 minutes
1 paper will be graded in 1 * 4/2
= 2 minutes
If 1 paper is graded in 2 minutes
x papers are graded in 60 minutes
x = 30 papers
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Calculate the area of the shape
Answer:
Step-by-step explanation:
Just divide the total shape into three shapes one rectangle and two triangles and then calculate the area
Hope this helps: )
find the answer to 9/16 in decimal form
Answer:
0.5625
Step-by-step explanation:
What is the price per bag of cookies
Answer: 6.3 per bag
Step-by-step explanation:
31.50 divided by 5 is 6.3!!!!
Answer: 6.3
Step-by-step explanation:
Divide 31.50 with 5
[tex]5\sqrt{31.50}[/tex]
5 goes into 3 0 times so you do 31/5. You get 6 with 1 as the remainder since 6x5 is 30. Now you do 15/5 which is 3. You get 63 but you have to add the decimal between the 6 and 3 so you will get 6.3. Hope this helped.
Anton surveys 80 students at his school and finds that 55% of them have mobile phones. He also finds that 98% of 50% adults have mobile phones. How many more adults than students ?
Answer:
13
Step-by-step explanation:
Student: 80 * 55% = 44
Adult: 50 * 98% = 49
49-44=5
Write the following series in sigma notation. 8+18+28+38+48
Answer:
in the image
Step-by-step explanation:
using the arithmetic formula
a = ao + d(n-1)
we can find the sum of this formula added up 5 times
X is a normal random variable with E[X] = -3 and V[X] = 4, compute a) ( ≤ 2.39) b) ( ≥ −2.39) c) (|| ≥ 2.39) d) (| + 3| ≥ 2.39) e) ( < 5) f) (|| < 5) g) With probability 0.33, variable X exceeds what value?
P(X ≤ 2.39)= 0.9967, P(X ≥ -2.39) = 0.3808, P(|X| ≥ 2.39) = 0.0388 ,P(|X + 3| ≥ 2.39) can be rewritten as P(X + 3 ≤ -2.39) + P(X + 3 ≥ 2.39)= 0.0388, P(X < 5) = 1 AND P(|X| < 5) = 0.34 with X is a normal random variable .
To solve the given problems, we need to standardize the normal random variable X using the formula Z = (X - μ)/σ, where μ is the mean and σ is the standard deviation.
a) P(X ≤ 2.39) = P(Z ≤ (2.39 - (-3))/2) = P(Z ≤ 2.695) = 0.9967
b) P(X ≥ -2.39) = P(Z ≥ (-2.39 - (-3))/2) = P(Z ≥ 0.305) = 0.3808
c) P(|X| ≥ 2.39) = P(X ≤ -2.39) + P(X ≥ 2.39) = P(Z ≤ (-2.39 - (-3))/2) + P(Z ≥ (2.39 - (-3))/2) = P(Z ≤ -1.805) + P(Z ≥ 2.695) = 0.0354 + 0.0034 = 0.0388
d) P(|X + 3| ≥ 2.39) can be rewritten as P(X + 3 ≤ -2.39) + P(X + 3 ≥ 2.39)
= P(Z ≤ (-2.39 - (-3))/2) + P(Z ≥ (2.39 - (-3))/2) = P(Z ≤ -1.805) + P(Z ≥ 2.695) = 0.0354 + 0.0034 = 0.0388
e) P(X < 5) = P(Z < (5 - (-3))/2) = P(Z < 4) = 1
f) P(|X| < 5) = P(-5 < X < 5) = P((-5 - (-3))/2 < Z < (5 - (-3))/2) = P(-4 < Z < 4) = 0.9987
g) Let the value that X exceeds with a probability of 0.33 be x. Then, we need to find the value of x such that P(X > x) = 0.33. Using the standard normal distribution table, we can find that the z-score for the 0.33 probability is 0.44. So, we can solve for x as follows:
0.33 = P(X > x) = P(Z > (x - (-3))/2) = P(Z > (x + 3)/2)
0.44 = 1 - P(Z ≤ (x + 3)/2)
P(Z ≤ (x + 3)/2) = 1 - 0.44 = 0.56
Using the standard normal distribution table, we can find that the z-score for the 0.56 probability is 0.17. So, we can solve for x as follows:
0.56 = P(Z ≤ (x + 3)/2) = P(Z ≤ (x + 3)/2)
0.17 = (x + 3)/2
x = 0.34
Therefore, with a probability of 0.33, variable X exceeds the value of 0.34.
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Alg 2 graphic quadratics in intercept form
The calculated key features of the quadratic functions 1 to 6 are listed below
Completing the key features of the graphsFunction 1: y = 1/2(x + 4)(x - 2)
Expand
y = x^2/2 + x - 4
From the function, we have
a = 1/2 (coefficient of x^2 term)
p = -b/2a (x-coordinate of the vertex)
p = -(1)/2(1/2)
p = -1
q = f(p) (y-coordinate of the vertex)
q = 1/2(1 + 4)(1 - 2)
q = -5/2
From the function, we have
x-intercepts = (-4, 0) and (2, 0)
This also means that the axis of symmetry is
x = -1
The quadratic function opens up because the coefficient of the x^2 term is positive.
Next, we have
Vertex = (-1, -5/2)
For the y-intercept, we have
y-intercept = f(0)
y-intercept = 1/2(0 + 4)(0 - 2)
y-intercept = -4
Slope to a point one unit from the vertex can be found by taking the derivative of the function:
f(x) = x^2/2 + x - 4
f'(x) = x + 1
At x = -2 (one unit to the left of the vertex), the slope is -1
i.e. f'(-2) = -2 + 1 = -1
At x = 0 (one unit to the right of the vertex), the slope is 1.
i.e. f'(0) = 0 + 1 = 1
When the above steps is repeated for the remaining functions, we have the following results:
Function 2: y = 1/2x(x - 8)
The features are:
a = 1/2, p = 4, q = -8x-intercepts = (0, 0) and (8, 0)Axis of symmetry: x = 4Opens up or down: UpVertex = (4, -8)y-intercepts = (0, 0)Slope to pt one unit from vertex: -1 and 1Function 3: y = (x + 2)(x - 2)
The features are:
a = 1, p = 0, q = -4x-intercepts = (-2, 0) and (2, 0)Axis of symmetry: x = 0Opens up or down: UpVertex = (0, -4)y-intercepts = (0, -4)Slope to pt one unit from vertex: -2 and 2Function 4: y = -1/3(x + 1)(x - 5)
The features are:
a = -1/3, p = 2, q = 3x-intercepts = (-1, 0) and (5, 0)Axis of symmetry: x = 2Opens up or down: DownVertex = (2, 3)y-intercepts = (0, 5/3)Slope to pt one unit from vertex: 2/3 and -2/3Function 5: y = 4(x + 2)(x + 1)
The features are:
a = 4, p = -3/2, q = -1x-intercepts = (-2, 0) and (-1, 0)Axis of symmetry: x = -3/2Opens up or down: UpVertex = (-3/2, -1)y-intercepts = (0, 8)Slope to pt one unit from vertex: -8 and 8Function 6: y = -(x - 3)(x - 3)
The features are:
a = -1, p = 3, q = 0x-intercepts = (3, 0)Axis of symmetry: x = 3Opens up or down: DownVertex = (3, 0)y-intercepts = (0, -9)Slope to pt one unit from vertex: 2 and -2Read more about quadratic functions at
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