Question 1 A) When factoring the expression 4x2y5+10x3y44x2y5+10x3y4 you determine that the greatest common factor is: (1 point) Responses 2x2y42x2y42 x squared y to the 4th power 14x5y914x5y914 x to the 5th power y to the 9th power 10x3y510x3y510 x cubed y to the 5th power 4xy4xy4 x y Question 2 A) Order the steps from first to last that would be used to factor: 3x2−13x−103x2−13x−10(7 points) Arrange responses in the correct order to answer the question. Select a response, navigate to the desired position and insert response at that position. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can be moved using the up and down arrow keys or by dragging with a mouse.  Find the two numbers that give a product of −30−30 and a sum of −13−13.  Final answer: (x−5)(3x+2)(x−5)(3x+2)  Replace the middle term with −15x−15x and 2x2x.  Determine if there is a greatest common factor amongst all the terms.  Factor by grouping: Take the greatest common factor out of the first two terms and the greatest common factor out of the last two terms to get 3x(x−5)+2(x−5)3x(x−5)+2(x−5)  Factor the common factor once more to get your final answer.  Multiply 3×−103×−10 Question 3 A)Fill in the blank to show what the quadratic expression would look like when factored.(5 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. x2−3x−10x2−3x−10 = (x−x−Response area)(x+x+Response area) 3x2−6x+93x2−6x+9 = Response area(x2−2x+3)(x2−2x+3) 9x2−259x2−25 = (3x−3x−Response area)(Response area+5+5) 1235103x9x Question 4 A) What are the x-intercepts of the quadratic equation below? y=(2x−3)(x−6)y=(2x−3)(x−6)(1 point) Responses (-1.5, 0) and (-6, 0) (-1.5, 0) and (-6, 0) (3, 0) and (6, 0) (3, 0) and (6, 0) (1.5, 0) and (6, 0) (1.5, 0) and (6, 0) (-3, 0) and (-6, 0) (-3, 0) and (-6, 0) Question 5 A) What are the solutions of the graph shown below? Select ALL that apply. (2 points) Responses x=2.5x=2.5x is equal to 2 point 5 x=−15x=−15x is equal to negative 15 x=−3x=−3x is equal to negative 3 x=3x=3x is equal to 3 x=−2.5x=−2.5x is equal to negative 2 point 5 Question 6 A)What is the minimum of the graph described by y=(x+4)2−5y=(x+4)2−5(1 point) Responses (-4, -5) (-4, -5) (-4, 5) (-4, 5) (4, -5) (4, -5) (4, 5) (4, 5) Question 7 A) Which equation has the same zeros as the function graphed? (1 point) Responses (x−2)2=y(x−2)2=yopen paren x minus 2 close paren squared is equal to y (x+5)(x + 2)=y(x+5)(x + 2)=y(x+5)(x + 2)=y(x+5)(x + 2)=y (x−2)2=(x+5)2+y(x−2)2=(x+5)2+yopen paren x minus 2 close paren squared is equal to open paren x plus 5 close paren squared plus y (x−2)(x−5)=y(x−2)(x−5)=yopen paren x minus 2 close paren times open paren x minus 5 close paren is equal to y Question 8 A)What are the zeros of the graph of y=2x2+5x−12y=2x2+5x−12?(1 point) Responses 3 and −43 and −43 and −43 and −4 −6 and 2−6 and 2−6 and 2−6 and 2 32 and−432 and−432 and−432 and−4 −35 and 4−35 and 4−35 and 4−35 and 4 Question 9 A)A rock is thrown from one side of a river to another. The function h(t) = −16t2 + 80t + 30 h(t) = −16t2 + 80t + 30 gives the height in inches of the rock t seconds after it has been thrown.(3 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. a) Find h(2.5)h(2.5). Response area b) What does h(2.5)h(2.5) represent in the context of this problem? Response area c) Does it make sense to find h(−10)h(−10) in the context of this problem? Response area 130301902.5 secondsThe time it takes for the height to be 2.5 inches above ground. The height of the rock 2.5 seconds after it has been thrown. The time it takes for the rock to hit the ground once it has been thrown. Yes, it makes sense because the height could be under sea level. No, it does not make sense because time cannot be negative. No, it does not make sense because we cannot have negative inches. Question 10 A)The function P(l) = −4l2 +32l − 52P(l) = −4l2 +32l − 52 gives the profit, in thousands, of producing ll units of lip gloss. What is the maximum profit that can be made? (1 point) Responses $4,000 $4,000 $208,000 $208,000 $32,000 $32,000 $12,000 $12,000 Question 11 A) Solve for x. Select all solutions. x2−64 = 0x2−64 = 0(2 points) Responses -8 -8 64 64 0 0 8 8 Question 12 A)Match the equation on the left to its equivalent on the right. (4 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. y=(x+3)2−8y=(x+3)2−8 y = x2+2x−8y = x2+2x−8 y = x2 − 10x + 16y = x2 − 10x + 16 y=(x+9)(x+1)y=(x+9)(x+1) y=x2+6x+1y=x2+6x+1y=x2+10x+9y=x2+10x+9y = (x+1)2−9y = (x+1)2−9y = (x−2)(x−8)y = (x−2)(x−8) Question 13 A) You are solving a quadratic by using the Quadratic Formula, What needs to be done to this function before we can identify a, b, and c? 7x2+2x=47x2+2x=4(1 point) Responses The like terms need to be combined. The like terms need to be combined. We need to add 4 on both sides of the equation. We need to add 4 on both sides of the equation. The quadratic first needs to be factored. The quadratic first needs to be factored. The equation needs to be set equal to zero. The equation needs to be set equal to zero. Question 14 A) When solving this quadratic by using the Quadratic Formula, what are the values of a, b, and c? 5x2 +12x =85x2 +12x =8(3 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. c a b 8512-8 Question 15 A) Place the steps in the correct order to solve the following equation using the quadratic formula. x2 − 10x = 12x2 − 10x = 12(6 points) Arrange responses in the correct order to answer the question. Select a response, navigate to the desired position and insert response at that position. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can be moved using the up and down arrow keys or by dragging with a mouse.  x=10±237√2x=10±2372  x=−(−10)±(−10)2−4(1)(−12)√2(1)x=−(−10)±(−10)2−4(1)(−12)2(1)  x=10±148√2x=10±1482  x=5±37−−√x=5±37  a = 1, b = -10, c = -12  x2−10x−12=0x2−10x−12=0 Question 16 A) You notice that the following quadratic equation cannot be factored, so you solve it by completing the square. What value of c would make the left-hand side of this equation a perfect square trinomial? x2 −8x + c = 13x2 −8x + c = 13(1 point) Responses 4 4 -4 -4 -8 -8 64 64 16 16

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Below are the responses for each question provided:

Question 1

A) The greatest common factor is: 2x²y⁴.

Question 2

A) Steps in order to factor $3x^2 - 13x - 10$:

Determine if there is a greatest common factor amongst all the terms.

Find the two numbers that give a product of -30 and a sum of -13.

Replace the middle term with -15x and 2x.

Factor by grouping: Take the greatest common factor out of the first two terms and the greatest common factor out of the last two terms to get $3x(x−5) + 2(x−5)$.

Factor the common factor once more to get your final answer.

Final answer: $ (x−5)(3x+2) $.

Multiply $3×−10$.

Question 3

A) Fill in the blank:

$x^2 - 3x - 10 = (x - 5)(x + 2)$

$3x^2 - 6x + 9 = (3)(x^2 - 2x + 3)$

$9x^2 - 25 = (3x - 5)(3x + 5)$

Question 4

A) The x-intercepts of $y=(2x−3)(x−6)$ are: (1.5, 0) and (6, 0).

Question 5

A) The solutions of the graph shown below select ALL that apply:

$x = 2.5$

$x = -3$

$x = 3$

Question 6

A) The minimum of the graph $y=(x+4)^2−5$ is: (-4, -5).

Question 7

A) The equation that has the same zeros as the function graphed is: (x−2)(x−5)=y.

Question 8

A) The zeros of the graph $y=2x^2 + 5x - 12$ are: 3 and -4.

Question 9

A) a) Find $h(2.5)$: 130.
b) What does $h(2.5)$ represent in the context of this problem?: The height of the rock 2.5 seconds after it has been thrown.
c) Does it make sense to find $h(-10)$?: No, it does not make sense because time cannot be negative.

Question 10

A) The maximum profit that can be made from $P(l) = -4l² + 32l - 52$ is: $12,000.

Question 11

A) Solve for x from $x² - 64 = 0$:

Solutions: -8, 8.

Question 12

A) Match the equation on the left to its equivalent on the right:

$y=(x+3)²−8$ → $y=x² + 6x + 1$

$y=x²−10x + 16$ → $y=(x−2)(x−8)$

Question 13

A) Before identifying $a$, $b$, and $c$ in $7x² + 2x = 4$, we need to: The equation needs to be set equal to zero.

Question 14

A) The values of $a$, $b$, and $c$ for $5x² + 12x = 8$ are:

$a = 5$

$b = 12$

$c = -8$

Question 15

A) Steps in the correct order to solve $x²−10x=12$ using the quadratic formula:

$x^2−10x−12=0$

Identify $a = 1, b = -10, c = -12$.

Use the quadratic formula: $x=\frac{-b±\sqrt{b^2−4ac}}{2a}$.

$x=10±\frac{√148}{2}$.

$x=5±\frac{√37}{1}$.

Final answer: $x=10±\frac{√(2)}{3}$.

Question 16

A) The value of $c$ that would make $x²−8x+c=13$ a perfect square trinomial is: 16.

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Question 1 A) When factoring the expression 4x2y5+10x3y44x2y5+10x3y4 you determine that the greatest common factor is: (1 point) Responses 2x2y42x2y42 x squared y to the 4th power 14x5y914x5y914 x to the 5th power y to the 9th power 10x3y510x3y510 x cubed y to the 5th power 4xy4xy4 x y Question 2 A) Order the steps from first to last that would be used to factor: 3x2−13x−103x2−13x−10(7 points) Arrange responses in the correct order to answer the question. Select a response, navigate to the desired position and insert response at that position. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can be moved using the up and down arrow keys or by dragging with a mouse.  Find the two numbers that give a product of −30−30 and a sum of −13−13.  Final answer: (x−5)(3x+2)(x−5)(3x+2)  Replace the middle term with −15x−15x and 2x2x.  Determine if there is a greatest common factor amongst all the terms.  Factor by grouping: Take the greatest common factor out of the first two terms and the greatest common factor out of the last two terms to get 3x(x−5)+2(x−5)3x(x−5)+2(x−5)  Factor the common factor once more to get your final answer.  Multiply 3×−103×−10 Question 3 A)Fill in the blank to show what the quadratic expression would look like when factored.(5 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. x2−3x−10x2−3x−10 = (x−x−Response area)(x+x+Response area) 3x2−6x+93x2−6x+9 = Response area(x2−2x+3)(x2−2x+3) 9x2−259x2−25 = (3x−3x−Response area)(Response area+5+5) 1235103x9x Question 4 A) What are the x-intercepts of the quadratic equation below? y=(2x−3)(x−6)y=(2x−3)(x−6)(1 point) Responses (-1.5, 0) and (-6, 0) (-1.5, 0) and (-6, 0) (3, 0) and (6, 0) (3, 0) and (6, 0) (1.5, 0) and (6, 0) (1.5, 0) and (6, 0) (-3, 0) and (-6, 0) (-3, 0) and (-6, 0) Question 5 A) What are the solutions of the graph shown below? Select ALL that apply. (2 points) Responses x=2.5x=2.5x is equal to 2 point 5 x=−15x=−15x is equal to negative 15 x=−3x=−3x is equal to negative 3 x=3x=3x is equal to 3 x=−2.5x=−2.5x is equal to negative 2 point 5 Question 6 A)What is the minimum of the graph described by y=(x+4)2−5y=(x+4)2−5(1 point) Responses (-4, -5) (-4, -5) (-4, 5) (-4, 5) (4, -5) (4, -5) (4, 5) (4, 5) Question 7 A) Which equation has the same zeros as the function graphed? (1 point) Responses (x−2)2=y(x−2)2=yopen paren x minus 2 close paren squared is equal to y (x+5)(x + 2)=y(x+5)(x + 2)=y(x+5)(x + 2)=y(x+5)(x + 2)=y (x−2)2=(x+5)2+y(x−2)2=(x+5)2+yopen paren x minus 2 close paren squared is equal to open paren x plus 5 close paren squared plus y (x−2)(x−5)=y(x−2)(x−5)=yopen paren x minus 2 close paren times open paren x minus 5 close paren is equal to y Question 8 A)What are the zeros of the graph of y=2x2+5x−12y=2x2+5x−12?(1 point) Responses 3 and −43 and −43 and −43 and −4 −6 and 2−6 and 2−6 and 2−6 and 2 32 and−432 and−432 and−432 and−4 −35 and 4−35 and 4−35 and 4−35 and 4 Question 9 A)A rock is thrown from one side of a river to another. The function h(t) = −16t2 + 80t + 30 h(t) = −16t2 + 80t + 30 gives the height in inches of the rock t seconds after it has been thrown.(3 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. a) Find h(2.5)h(2.5). Response area b) What does h(2.5)h(2.5) represent in the context of this problem? Response area c) Does it make sense to find h(−10)h(−10) in the context of this problem? Response area 130301902.5 secondsThe time it takes for the height to be 2.5 inches above ground. The height of the rock 2.5 seconds after it has been thrown. The time it takes for the rock to hit the ground once it has been thrown. Yes, it makes sense because the height could be under sea level. No, it does not make sense because time cannot be negative. No, it does not make sense because we cannot have negative inches. Question 10 A)The function P(l) = −4l2 +32l − 52P(l) = −4l2 +32l − 52 gives the profit, in thousands, of producing ll units of lip gloss. What is the maximum profit that can be made? (1 point) Responses $4,000 $4,000 $208,000 $208,000 $32,000 $32,000 $12,000 $12,000 Question 11 A) Solve for x. Select all solutions. x2−64 = 0x2−64 = 0(2 points) Responses -8 -8 64 64 0 0 8 8 Question 12 A)Match the equation on the left to its equivalent on the right. (4 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. y=(x+3)2−8y=(x+3)2−8 y = x2+2x−8y = x2+2x−8 y = x2 − 10x + 16y = x2 − 10x + 16 y=(x+9)(x+1)y=(x+9)(x+1) y=x2+6x+1y=x2+6x+1y=x2+10x+9y=x2+10x+9y = (x+1)2−9y = (x+1)2−9y = (x−2)(x−8)y = (x−2)(x−8) Question 13 A) You are solving a quadratic by using the Quadratic Formula, What needs to be done to this function before we can identify a, b, and c? 7x2+2x=47x2+2x=4(1 point) Responses The like terms need to be combined. The like terms need to be combined. We need to add 4 on both sides of the equation. We need to add 4 on both sides of the equation. The quadratic first needs to be factored. The quadratic first needs to be factored. The equation needs to be set equal to zero. The equation needs to be set equal to zero. Question 14 A) When solving this quadratic by using the Quadratic Formula, what are the values of a, b, and c? 5x2 +12x =85x2 +12x =8(3 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. c a b 8512-8 Question 15 A) Place the steps in the correct order to solve the following equation using the quadratic formula. x2 − 10x = 12x2 − 10x = 12(6 points) Arrange responses in the correct order to answer the question. Select a response, navigate to the desired position and insert response at that position. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can be moved using the up and down arrow keys or by dragging with a mouse.  x=10±237√2x=10±2372  x=−(−10)±(−10)2−4(1)(−12)√2(1)x=−(−10)±(−10)2−4(1)(−12)2(1)  x=10±148√2x=10±1482  x=5±37−−√x=5±37  a = 1, b = -10, c = -12  x2−10x−12=0x2−10x−12=0 Question 16 A) You notice that the following quadratic equation cannot be factored, so you solve it by completing the square. What value of c would make the left-hand side of this equation a perfect square trinomial? x2 −8x + c = 13x2 −8x + c = 13(1 point) Responses 4 4 -4 -4 -8 -8 64 64 16 16

1 answer

Below are the responses for each question provided:

Question 1

A) The greatest common factor is: 2x²y⁴.

Question 2

A) Steps in order to factor $3x^2 - 13x - 10$:

Determine if there is a greatest common factor amongst all the terms.
Find the two numbers that give a product of -30 and a sum of -13.
Replace the middle term with -15x and 2x.
Factor by grouping: Take the greatest common factor out of the first two terms and the greatest common factor out of the last two terms to get $3x(x−5) + 2(x−5)$.
Factor the common factor once more to get your final answer.
Final answer: $ (x−5)(3x+2) $.
Multiply $3×−10$.

Question 3

A) Fill in the blank:

$x^2 - 3x - 10 = (x - 5)(x + 2)$
$3x^2 - 6x + 9 = (3)(x^2 - 2x + 3)$
$9x^2 - 25 = (3x - 5)(3x + 5)$

Question 4

A) The x-intercepts of $y=(2x−3)(x−6)$ are: (1.5, 0) and (6, 0).

Question 5

A) The solutions of the graph shown below select ALL that apply:

$x = 2.5$
$x = -3$
$x = 3$

Question 6

A) The minimum of the graph $y=(x+4)^2−5$ is: (-4, -5).

Question 7

A) The equation that has the same zeros as the function graphed is: (x−2)(x−5)=y.

Question 8

A) The zeros of the graph $y=2x^2 + 5x - 12$ are: 3 and -4.

Question 9

A) a) Find $h(2.5)$: 130.
b) What does $h(2.5)$ represent in the context of this problem?: The height of the rock 2.5 seconds after it has been thrown.
c) Does it make sense to find $h(-10)$?: No, it does not make sense because time cannot be negative.

Question 10

A) The maximum profit that can be made from $P(l) = -4l² + 32l - 52$ is: $12,000.

Question 11

A) Solve for x from $x² - 64 = 0$:

Solutions: -8, 8.

Question 12

A) Match the equation on the left to its equivalent on the right:

$y=(x+3)²−8$ → $y=x² + 6x + 1$
$y=x²−10x + 16$ → $y=(x−2)(x−8)$

Question 13

A) Before identifying $a$, $b$, and $c$ in $7x² + 2x = 4$, we need to: The equation needs to be set equal to zero.

Question 14

A) The values of $a$, $b$, and $c$ for $5x² + 12x = 8$ are:

$a = 5$
$b = 12$
$c = -8$

Question 15

A) Steps in the correct order to solve $x²−10x=12$ using the quadratic formula:

$x^2−10x−12=0$
Identify $a = 1, b = -10, c = -12$.
Use the quadratic formula: $x=\frac{-b±\sqrt{b^2−4ac}}{2a}$.
$x=10±\frac{√148}{2}$.
$x=5±\frac{√37}{1}$.
Final answer: $x=10±\frac{√(2)}{3}$.

Question 16

A) The value of $c$ that would make $x²−8x+c=13$ a perfect square trinomial is: 16.

Ask a New Question or answer this question.

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