Question 2 A) What are the x-intercepts of the function below? g(x)=(4x−1)(x+2)g(x)=(4x−1)(x+2)(1 point) Responses (-0.25, 0) and (2, 0) (-0.25, 0) and (2, 0) (1, 0) and (2, 0) (1, 0) and (2, 0) (-1, 0) and (2, 0) (-1, 0) and (2, 0) (0.25, 0) and (-2, 0) (0.25, 0) and (-2, 0) Question 3 A) What are the solutions of the graph below? Select ALL that apply. (2 points) Responses y = 4y = 4y = 4y = 4 x=−3x=−3x is equal to negative 3 x = 3x = 3x = 3x = 3 x = 4x = 4x = 4x = 4 x = −4x = −4x = −4x = −4 Question 4 A)What is the minimum of the graph described by y=(x+7)2 +3y=(x+7)2 +3?(1 point) Responses (7, 3)(7, 3)(7, 3)(7, 3) (−7, 3)(−7, 3)(−7, 3)(−7, 3) (−7, −3)(−7, −3)(−7, −3)(−7, −3) (7, −3)(7, −3)(7, −3)(7, −3) Question 5 A) Which equation has the same zeros as the function graphed? (1 point) Responses −(x+3)(x+7)=y−(x+3)(x+7)=ynegative open paren x plus 3 close paren times open paren x plus 7 close paren is equal to y −(x−3)(x−7)= y−(x−3)(x−7)= y−(x−3)(x−7)= y−(x−3)(x−7)= y (x−7)2=(x−3)2+y(x−7)2=(x−3)2+yopen paren x minus 7 close paren squared is equal to open paren x minus 3 close paren squared plus y (x+3)(x + 7)=y(x+3)(x + 7)=y(x+3)(x + 7)=y(x+3)(x + 7)=y Question 6 A)What are the zeros of the graph of y = 4x2 +9x −9y = 4x2 +9x −9?(1 point) Responses 4 and −94 and −94 and −94 and −9 −34 and 3−34 and 3−34 and 3−34 and 3 −36 and 4−36 and 4−36 and 4−36 and 4 34 and−334 and−334 and−334 and−3 Question 7 A) Answer the questions about the key characteristics of the function below. (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. Axis of Symmetry: Response area Does this function have a minimum or maximum? Response area x-Intercepts Response area y-intercept Response area MinimumMaximumx = 1.5x = 1.5y=4y=4(0,-5)(0.5,0) and (2.5,0)(-5,0)(0,0.5) and (0,2.5) Question 8 A) Solve for x. Select all solutions. x2−25 = 0x2−25 = 0(1 point) Responses ±5–√±5plus or minus square root of 5 -5 -5 5 5 25 25 0 0 Question 9 A) Which of the following is a solution? (x−3)2−81=0(x−3)2−81=0(1 point) Responses 12 12 -12 -12 -3 -3 3 3 Question 10 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+4)2−5y=(x+4)2−5 y = x2 − 1x −20y = x2 − 1x −20 y = x2−6x+16y = x2−6x+16 y=(x+8)(x+11)y=(x+8)(x+11) y=x2+19x+88y=x2+19x+88y = (x−3)2+7y = (x−3)2+7y=x2+8x+11y=x2+8x+11y = (x+4)(x−5)y = (x+4)(x−5) Question 11 A) You notice that the following problem 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 −14x + c = 13x2 −14x + c = 13(1 point) Responses 4 4 -7 -7 -14 -14 196 196 49 49 Question 12 A)(8 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. Fill in the steps to complete the square: x2 +12x − 14 = 0x2 +12x − 14 = 0 x2 + 12x = 14x2 + 12x = 14 x2 +12x + x2 +12x + Response area = 14+ = 14+ Response area We factor and simplify to get: (x+6)2 =(x+6)2 = Response area At this point, we need to Response area After that is done, we will have: Response area == Response area We get isolate the variable by: Response area Final answers are: Response area (x+12)2(x+12)2square both sides of the equation. (x+6)2(x+6)2±50−−√±5012subtracting 12 from both sides of the equation.112x+12−−−−−√x+12subtracting 6 from both sides of the equation. 144-22x+6−−−−−√x+6take the square root of both sides of the equation.50−12 & 0−12 & 017x+6x+6±12±1236−6±50−−√−6±50x+12x+12100−6±36−−√−6±36±36−−√±36 Question 13 A) When solving this quadratic by using the Quadratic Formula, what are the values of a, b, and c? −3x2 +10x =−9−3x2 +10x =−9(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 b c -310-99 Question 14 A)How many solution are in the solution set for the equation 2x2=202x2=20(1 point) Responses Zero Zero Infinitely many Infinitely many One One Two Two Question 15 A)Based on the Zero Product Property, which of the following statements must be true about the quadratic equation (3x+4)(x−2)=0(3x+4)(x−2)=0 (1 point) Responses No values of x will make the function equal to 0 No values of x will make the function equal to 0 Neither of the factors, (3x+4) or (x-2), must equal 0 for the entire function to equal 0. Neither of the factors, (3x+4) or (x-2), must equal 0 for the entire function to equal 0. At least one of the factors (3x+4) or (x-2), must equal 0 for the entire function to equal 0. At least one of the factors (3x+4) or (x-2), must equal 0 for the entire function to equal 0. Both factors, (3x+4) and (x-2), must equal 0 for the entire function to equal 0. Both factors, (3x+4) and (x-2), must equal 0 for the entire function to equal 0. Question 16 A)Factor the quadratic expression 2x2+7x+32x2+7x+3(1 point) Responses (2x+3)(x+1) (2x+3)(x+1) (2x+1)(2x+3) (2x+1)(2x+3) (2x+1)(x+3) (2x+1)(x+3) (2x+7)(x+3) (2x+7)(x+3) Question 17 A)Determine where the values 4 and 6 are solutions to the quadratic equation x2−10x+24x2−10x+24, and then select the correct answer from the following options.(1 point) Responses Both x=4 and x=6 are solutions Both x=4 and x=6 are solutions Neither x=4 nor x=6 is a solution. Neither x=4 nor x=6 is a solution. Only x=6 is a solution Only x=6 is a solution Only x=4 is a solution Only x=4 is a solution

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Here are the answers to the questions based on the provided information:

Question 2 A) The x-intercepts of the function \( g(x) = (4x - 1)(x + 2) \) can be found by setting each factor equal to zero:

\( 4x - 1 = 0 \rightarrow 4x = 1 \rightarrow x = \frac{1}{4} = 0.25 \)

\( x + 2 = 0 \rightarrow x = -2 \)

The x-intercepts are therefore \( (0.25, 0) \) and \( (-2, 0) \).

Responses: (0.25, 0) and (-2, 0)

Question 3 A) Without the graph provided, we cannot determine the exact solutions. Assuming that this is a typical context, I would recommend looking for points where the graph intersects the x-axis. However, I cannot accurately answer this without visual information.

Question 4 A) The minimum of the graph described by \( y = (x + 7)^2 + 3 \) occurs at the vertex, which is at the point \( (-7, 3) \).

Responses: (-7, 3)

Question 5 A) Without the graph, I cannot state which equation has the same zeros as the function graphed. Normally, you would look for the factors of the graph that intersect the x-axis.

Question 6 A) To find the zeros of \( y = 4x^2 + 9x - 9 \), use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). Here, \( a = 4 \), \( b = 9 \), and \( c = -9 \).

Calculate the discriminant: \( b^2 - 4ac = 9^2 - 4(4)(-9) = 81 + 144 = 225 \)

\( x = \frac{-9 \pm \sqrt{225}}{2(4)} = \frac{-9 \pm 15}{8} \)

This results in two solutions:

\( x = \frac{-9 + 15}{8} = \frac{6}{8} = \frac{3}{4} \)

\( x = \frac{-9 - 15}{8} = \frac{-24}{8} = -3 \)

Responses: \( \frac{3}{4} \) and \( -3 \)

Question 7 A) The key characteristics of the function need to be filled based on provided values.

Axis of Symmetry: \( x = 1.5 \)

Does this function have a minimum or maximum? Minimum

x-Intercepts: \( (0.5, 0) \) and \( (2.5, 0) \)

y-Intercept: \( (0, -5) \)

Question 8 A) To solve \( x^2 - 25 = 0 \):

Factor: \( (x - 5)(x + 5) = 0 \)

Solutions: \( x = \pm 5 \)

Responses: \( \pm 5 \)

Question 9 A) For \( (x - 3)^2 - 81 = 0 \):

This can be rearranged to \( (x - 3)^2 = 81 \).

Therefore, \( x - 3 = \pm 9 \) gives \( x = 12 \) or \( x = -6 \).

Responses: 12 and -6

Question 10 A) Without the options presented, I cannot match the equations. If given specific equations, I would seek common factors or roots.

Question 11 A) In the equation \( x^2 - 14x + c = 13 \), to make it a perfect square:

The term needed is \(\left(\frac{-14}{2}\right)^2 = 49\), thus \( c = 49 \).

Responses: 49

Question 12 A) The steps to complete the square for \( x^2 + 12x - 14 = 0 \) are as follows:

\( x^2 + 12x = 14 \)

Add \( 36 \) to both sides (which is \( \left(\frac{12}{2}\right)^2 \)): \( x^2 + 12x + 36 = 50 \)

We factor to get \( (x + 6)^2 = 50 \)

Take square root and then isolate variable: \( x + 6 = \pm\sqrt{50} \)

Final answers are: \( x = -6 \pm \sqrt{50} \)

Question 13 A) In the quadratic equation provided, we have:

\( a = -3 \)

\( b = 10 \)

\( c = 9 \) (rearranging the equation gives \( +9 \))

Question 14 A) For the equation \( 2x^2 = 20 \):

Dividing gives \( x^2 = 10 \).

There are two solutions, \( x = \pm\sqrt{10} \).

Responses: Two

Question 15 A) Based on the Zero Product Property:

Response: At least one of the factors (3x + 4) or (x - 2) must equal 0 for the entire function to equal 0.

Question 16 A) To factor the quadratic expression \( 2x^2 + 7x + 3 \), we can look for factors of \( 2 \cdot 3 \) (which is 6) that add up to 7. This leads to:

\( (2x + 1)(x + 3) \)

Responses: (2x + 1)(x + 3)

Question 17 A) We can check if \( x = 4 \) and \( x = 6 \) are solutions of the equation \( x^2 - 10x + 24 \):

Substituting \( x = 4 \): \( 16 - 40 + 24 = 0 \) (Yes)

Substituting \( x = 6 \): \( 36 - 60 + 24 = 0 \) (Yes)

Responses: Both \( x=4 \) and \( x=6 \) are solutions.

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Question 2 A) What are the x-intercepts of the function below? g(x)=(4x−1)(x+2)g(x)=(4x−1)(x+2)(1 point) Responses (-0.25, 0) and (2, 0) (-0.25, 0) and (2, 0) (1, 0) and (2, 0) (1, 0) and (2, 0) (-1, 0) and (2, 0) (-1, 0) and (2, 0) (0.25, 0) and (-2, 0) (0.25, 0) and (-2, 0) Question 3 A) What are the solutions of the graph below? Select ALL that apply. (2 points) Responses y = 4y = 4y = 4y = 4 x=−3x=−3x is equal to negative 3 x = 3x = 3x = 3x = 3 x = 4x = 4x = 4x = 4 x = −4x = −4x = −4x = −4 Question 4 A)What is the minimum of the graph described by y=(x+7)2 +3y=(x+7)2 +3?(1 point) Responses (7, 3)(7, 3)(7, 3)(7, 3) (−7, 3)(−7, 3)(−7, 3)(−7, 3) (−7, −3)(−7, −3)(−7, −3)(−7, −3) (7, −3)(7, −3)(7, −3)(7, −3) Question 5 A) Which equation has the same zeros as the function graphed? (1 point) Responses −(x+3)(x+7)=y−(x+3)(x+7)=ynegative open paren x plus 3 close paren times open paren x plus 7 close paren is equal to y −(x−3)(x−7)= y−(x−3)(x−7)= y−(x−3)(x−7)= y−(x−3)(x−7)= y (x−7)2=(x−3)2+y(x−7)2=(x−3)2+yopen paren x minus 7 close paren squared is equal to open paren x minus 3 close paren squared plus y (x+3)(x + 7)=y(x+3)(x + 7)=y(x+3)(x + 7)=y(x+3)(x + 7)=y Question 6 A)What are the zeros of the graph of y = 4x2 +9x −9y = 4x2 +9x −9?(1 point) Responses 4 and −94 and −94 and −94 and −9 −34 and 3−34 and 3−34 and 3−34 and 3 −36 and 4−36 and 4−36 and 4−36 and 4 34 and−334 and−334 and−334 and−3 Question 7 A) Answer the questions about the key characteristics of the function below. (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. Axis of Symmetry: Response area Does this function have a minimum or maximum? Response area x-Intercepts Response area y-intercept Response area MinimumMaximumx = 1.5x = 1.5y=4y=4(0,-5)(0.5,0) and (2.5,0)(-5,0)(0,0.5) and (0,2.5) Question 8 A) Solve for x. Select all solutions. x2−25 = 0x2−25 = 0(1 point) Responses ±5–√±5plus or minus square root of 5 -5 -5 5 5 25 25 0 0 Question 9 A) Which of the following is a solution? (x−3)2−81=0(x−3)2−81=0(1 point) Responses 12 12 -12 -12 -3 -3 3 3 Question 10 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+4)2−5y=(x+4)2−5 y = x2 − 1x −20y = x2 − 1x −20 y = x2−6x+16y = x2−6x+16 y=(x+8)(x+11)y=(x+8)(x+11) y=x2+19x+88y=x2+19x+88y = (x−3)2+7y = (x−3)2+7y=x2+8x+11y=x2+8x+11y = (x+4)(x−5)y = (x+4)(x−5) Question 11 A) You notice that the following problem 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 −14x + c = 13x2 −14x + c = 13(1 point) Responses 4 4 -7 -7 -14 -14 196 196 49 49 Question 12 A)(8 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. Fill in the steps to complete the square: x2 +12x − 14 = 0x2 +12x − 14 = 0 x2 + 12x = 14x2 + 12x = 14 x2 +12x + x2 +12x + Response area = 14+ = 14+ Response area We factor and simplify to get: (x+6)2 =(x+6)2 = Response area At this point, we need to Response area After that is done, we will have: Response area == Response area We get isolate the variable by: Response area Final answers are: Response area (x+12)2(x+12)2square both sides of the equation. (x+6)2(x+6)2±50−−√±5012subtracting 12 from both sides of the equation.112x+12−−−−−√x+12subtracting 6 from both sides of the equation. 144-22x+6−−−−−√x+6take the square root of both sides of the equation.50−12 & 0−12 & 017x+6x+6±12±1236−6±50−−√−6±50x+12x+12100−6±36−−√−6±36±36−−√±36 Question 13 A) When solving this quadratic by using the Quadratic Formula, what are the values of a, b, and c? −3x2 +10x =−9−3x2 +10x =−9(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 b c -310-99 Question 14 A)How many solution are in the solution set for the equation 2x2=202x2=20(1 point) Responses Zero Zero Infinitely many Infinitely many One One Two Two Question 15 A)Based on the Zero Product Property, which of the following statements must be true about the quadratic equation (3x+4)(x−2)=0(3x+4)(x−2)=0 (1 point) Responses No values of x will make the function equal to 0 No values of x will make the function equal to 0 Neither of the factors, (3x+4) or (x-2), must equal 0 for the entire function to equal 0. Neither of the factors, (3x+4) or (x-2), must equal 0 for the entire function to equal 0. At least one of the factors (3x+4) or (x-2), must equal 0 for the entire function to equal 0. At least one of the factors (3x+4) or (x-2), must equal 0 for the entire function to equal 0. Both factors, (3x+4) and (x-2), must equal 0 for the entire function to equal 0. Both factors, (3x+4) and (x-2), must equal 0 for the entire function to equal 0. Question 16 A)Factor the quadratic expression 2x2+7x+32x2+7x+3(1 point) Responses (2x+3)(x+1) (2x+3)(x+1) (2x+1)(2x+3) (2x+1)(2x+3) (2x+1)(x+3) (2x+1)(x+3) (2x+7)(x+3) (2x+7)(x+3) Question 17 A)Determine where the values 4 and 6 are solutions to the quadratic equation x2−10x+24x2−10x+24, and then select the correct answer from the following options.(1 point) Responses Both x=4 and x=6 are solutions Both x=4 and x=6 are solutions Neither x=4 nor x=6 is a solution. Neither x=4 nor x=6 is a solution. Only x=6 is a solution Only x=6 is a solution Only x=4 is a solution Only x=4 is a solution

1 answer

Here are the answers to the questions based on the provided information:

Question 2 A) The x-intercepts of the function \( g(x) = (4x - 1)(x + 2) \) can be found by setting each factor equal to zero:

\( 4x - 1 = 0 \rightarrow 4x = 1 \rightarrow x = \frac{1}{4} = 0.25 \)
\( x + 2 = 0 \rightarrow x = -2 \)

The x-intercepts are therefore \( (0.25, 0) \) and \( (-2, 0) \).

Responses: (0.25, 0) and (-2, 0)

Question 3 A) Without the graph provided, we cannot determine the exact solutions. Assuming that this is a typical context, I would recommend looking for points where the graph intersects the x-axis. However, I cannot accurately answer this without visual information.

Question 4 A) The minimum of the graph described by \( y = (x + 7)^2 + 3 \) occurs at the vertex, which is at the point \( (-7, 3) \).

Responses: (-7, 3)

Question 5 A) Without the graph, I cannot state which equation has the same zeros as the function graphed. Normally, you would look for the factors of the graph that intersect the x-axis.

Question 6 A) To find the zeros of \( y = 4x^2 + 9x - 9 \), use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). Here, \( a = 4 \), \( b = 9 \), and \( c = -9 \).

Calculate the discriminant: \( b^2 - 4ac = 9^2 - 4(4)(-9) = 81 + 144 = 225 \)
\( x = \frac{-9 \pm \sqrt{225}}{2(4)} = \frac{-9 \pm 15}{8} \)

This results in two solutions:

\( x = \frac{-9 + 15}{8} = \frac{6}{8} = \frac{3}{4} \)
\( x = \frac{-9 - 15}{8} = \frac{-24}{8} = -3 \)

Responses: \( \frac{3}{4} \) and \( -3 \)

Question 7 A) The key characteristics of the function need to be filled based on provided values.

Axis of Symmetry: \( x = 1.5 \)
Does this function have a minimum or maximum? Minimum
x-Intercepts: \( (0.5, 0) \) and \( (2.5, 0) \)
y-Intercept: \( (0, -5) \)

Question 8 A) To solve \( x^2 - 25 = 0 \):

Factor: \( (x - 5)(x + 5) = 0 \)
Solutions: \( x = \pm 5 \)

Responses: \( \pm 5 \)

Question 9 A) For \( (x - 3)^2 - 81 = 0 \):

This can be rearranged to \( (x - 3)^2 = 81 \).
Therefore, \( x - 3 = \pm 9 \) gives \( x = 12 \) or \( x = -6 \).

Responses: 12 and -6

Question 10 A) Without the options presented, I cannot match the equations. If given specific equations, I would seek common factors or roots.

Question 11 A) In the equation \( x^2 - 14x + c = 13 \), to make it a perfect square:

The term needed is \(\left(\frac{-14}{2}\right)^2 = 49\), thus \( c = 49 \).

Responses: 49

Question 12 A) The steps to complete the square for \( x^2 + 12x - 14 = 0 \) are as follows:

\( x^2 + 12x = 14 \)
Add \( 36 \) to both sides (which is \( \left(\frac{12}{2}\right)^2 \)): \( x^2 + 12x + 36 = 50 \)
We factor to get \( (x + 6)^2 = 50 \)
Take square root and then isolate variable: \( x + 6 = \pm\sqrt{50} \)
Final answers are: \( x = -6 \pm \sqrt{50} \)

Question 13 A) In the quadratic equation provided, we have:

\( a = -3 \)
\( b = 10 \)
\( c = 9 \) (rearranging the equation gives \( +9 \))

Question 14 A) For the equation \( 2x^2 = 20 \):

Dividing gives \( x^2 = 10 \).
There are two solutions, \( x = \pm\sqrt{10} \).

Responses: Two

Question 15 A) Based on the Zero Product Property:

Response: At least one of the factors (3x + 4) or (x - 2) must equal 0 for the entire function to equal 0.

Question 16 A) To factor the quadratic expression \( 2x^2 + 7x + 3 \), we can look for factors of \( 2 \cdot 3 \) (which is 6) that add up to 7. This leads to:

\( (2x + 1)(x + 3) \)

Responses: (2x + 1)(x + 3)

Question 17 A) We can check if \( x = 4 \) and \( x = 6 \) are solutions of the equation \( x^2 - 10x + 24 \):

Substituting \( x = 4 \): \( 16 - 40 + 24 = 0 \) (Yes)
Substituting \( x = 6 \): \( 36 - 60 + 24 = 0 \) (Yes)

Responses: Both \( x=4 \) and \( x=6 \) are solutions.

GPT-4o mini · Answer