question

What are the solutions of 3x2 + 14x + 16 = 0?

answer

B

question

The only solution of the equation x2 + bx + 16 = 0 is x = 4. What is the value of b?

answer

b = -8

question

Which function has zeros at x = β2 and x = 5?

answer

f(x) = x2 β 3x β 10

question

An equation has solutions of m = -5 and m = 9. Which could be the equation?

answer

(m + 5)(m - 9) = 0

question

What are the solutions to x2 + 8x + 7 = 0?

answer

x = -7 and x = -1

question

Which equations are true for x = -2 and x = 2? Check all that apply.

answer

x2 - 4 = 0
4x2 = 16

question

Which function has zeros at x = 10 and x = 2?

answer

f(x) = x2 - 12x + 20

question

John has 48 square centimeter tiles he wants to use to create a mosaic. He wants the mosaic to be rectangular with a length that is 2 centimeters longer than the width.
Which equation could John solve to find w, the greatest width in centimeters he can use for the mosaic?

answer

w(w + 2) = 48

question

For what values of x is x2 + 2x = 24 true?

answer

4 and -6

question

What is the only solution of 2x2 + 8x = x2 - 16?

answer

-4

question

Which is a solution to (x β 2)(x + 10) = 13?

answer

x = 3

question

Which is a solution to the equation?
(x β2)(x + 5) = 18

answer

x = β7

question

Which is a solution to (x - 3)(x + 9) = -27?

answer

x = 0

question

What are the solutions to the equation?
x2 + 6x = 40

answer

x = β10 and x = 4

question

Two factors of -48 have a difference of 19. The factor with a greater absolute value is positive.
What is the sum of the factors?

answer

13

question

What are the solutions to the quadratic equation x2 - 16 = 0?

answer

x = 4 and x = -4

question

What are the solutions to the quadratic equation 3(x β 4)2 = 75?

answer

x = β1 and x = 9

question

What are the solutions of the quadratic equation (x + 3)2 = 49?

answer

x = 4 and x = -10

question

What are the solution(s) to the quadratic equation x2 - 25 = 0?

answer

x = 5 and x = -5

question

Which are the roots of the quadratic function f(b) = b2 - 75? Check all that apply.

answer

1and 2

question

Theo started to solve the quadratic equation (x + 2)2 - 9 = -5. He added 9 to both sides and the resulting equation was
(x + 2)2 = 4. Next, he took the square root of each side.
Which was the resulting equation of that step?

answer

x + 2 = Β±2

question

Which are the roots of the quadratic function f(q) = q2 - 125? Check all that apply.

answer

1 and 2

question

What are the solution(s) of the quadratic equation 98 - x2 = 0?

answer

C.

question

What are the solutions to the quadratic equation (5y + 6)2 = 24?

answer

A.

question

What value of c makes x2 β 24x + c a perfect square trinomial?

answer

144

question

Solve x2 + 14x = β24 by completing the square.
What is the solution set of the equation?

answer

{β12, β2}

question

Solve x2 - 8x = 3 by completing the square. Which is the solution set of the equation?

answer

A.

question

Which are the solutions of x2 = 19x + 1?

answer

B.

question

What value of c makes x2 β 12x + c a perfect square trinomial?

answer

36

question

Solve x2 = 12x - 15 by completing the square. Which is the solution set of the equation?

answer

D.

question

What value of c makes x2 + 6x + c a perfect square trinomial?

answer

9

question

Which are the solutions of x2 = -7x - 8?

answer

D.

question

Atraeus is solving the quadratic equation by completing the square. What is the value of A.

answer

7

question

What are the zeros of the quadratic function f(x)=2x2-10x-3

answer

C

question

Sienne is solving the quadratic equation by completing the square. What is the value of A.

answer

3

question

Patel is solving 8x2+16x+3=0 check all that apply

answer

1,2,5

question

The first few steps in solving the quadratic equation 8x2+80x=-5 by completing the square are shown.

answer

200

question

Atraeus is solving the quadratic equation by completing the square.
7x2 - 14x + 6 = 0
7x2 - 14x = -6
A(x2 - 2x) = -6
What is the value of A?

answer

7

question

What are the zeros of the quadratic function f(x) = 2x2 - 10x - 3?

answer

c.

question

Isoke is solving the quadratic equation by completing the square.
10x2 + 40x - 13 = 0
10x2 + 40x = 13
A(x2 + 4x) = 13
What is the value of A?

answer

10

question

Sunil is solving the quadratic equation by completing the square. What should sunil do next.

answer

C.

question

What are the zeros of the quadratic function f(x)=2x2+16x-9

answer

Not b

question

What are the zeros of the quadratic function f(x)=6x2+12x-7

answer

Not d

question

What are the zeros of the quadratic function f(x)=16x2+32x-9

answer

B.

question

Lie is solving a quadratic equation by completing the square. What should lie do next

answer

B.

question

Which is a zero of the quadratic function f(x)=9x2-54x-19

answer

Not b

question

In which step did yvonne make a mistake.

answer

A.

question

In which step did tran first make an error.

answer

Not d

question

What should gio do first.

answer

A.

question

What should maya do first

answer

C.

question

Which statement is true about the quadratic equation 8x2 β 5x + 3 = 0?

answer

The leading coefficient is 8.

question

Determine the discriminant for the quadratic equation 0 = -2x2 + 3. Based on the discriminant value, how many real number solutions does the equation have?
Discriminant = b2 - 4ac

answer

2

question

The first step for deriving the quadratic formula from the quadratic equation, 0 = ax2 + bx + c, is shown.
Step 1: -c = ax2 + bx
Which best explains or justifies Step 1?

answer

subtraction property of equality

question

What are the values of a, b, and c in the quadratic equation -2x2 + 4x - 3 = 0?

answer

a = -2, b = 4, c = - 3

question

What is the value of the discriminant for the quadratic equation -3 = -x2 + 2x?
Discriminant = b2 - 4ac

answer

not c

question

What are the values of a, b, and c in the quadratic equation 0 = 5x - 4x2 - 2?

answer

a = -4, b = 5, c = -2

question

Which shows the correct substitution of the values a, b, and c from the equation 0 = - 3x2 - 2x + 6 into the quadratic formula?
Quadratic formula: x =

answer

not c or b

question

What is the value of the discriminant for the quadratic equation 0 = 2x2 + x - 3?
Discriminant = b2 - 4ac

answer

not a

question

Which shows the correct substitution of the values a, b, and c from the equation 1 = -2x + 3x2 + 1 into the quadratic formula?
Quadratic formula:

answer

not d

question

What is the value of the discriminant, b2 β 4ac, for the quadratic equation 0 = x2 β 4x + 5, and what does it mean about the number of real solutions the equation has?

answer

The discriminant is β4, so the equation has no real solutions

question

What is the value of the discriminant for the quadratic equation 0 = x + 2 + x2?
Discriminant = b2 - 4ac

answer

-7

question

Which shows the correct substitution of the values a, b, and c from the equation -2 = -x + x2 - 4 into the quadratic formula?
Quadratic formula: x =

answer

not c

question

A student is deriving the quadratic formula. Her first two steps are shown.
Step 1: -c = ax2 + bx
Step 2:
Which best explains or justifies Step 2?

answer

factoring the binomial

question

Alessandro wrote the quadratic equation -6 = x2 + 4x - 1 in standard form. What is the value of c in his new equation?

answer

not -1

question

Some of the steps in the derivation of the quadratic formula are shown.
Step 4:
Step 5:
Step 6:
Step 7:
Which best explains why the expression cannot be rewritten as during the next step?

answer

not d

question

Which shows the correct substitution of the values a, b, and c from the equation 1 = -2x + 3x2 + 1 into the quadratic formula?
Quadratic formula:

answer

a.

question

What are the values of a, b, and c in the quadratic equation 0 = x2 - 3x - 2?

answer

a =1/2 , b = -3, c = -2

question

Some of the steps in the derivation of the quadratic formula are shown.
Step 3: -c + = a
Step 4a: -c + = a
Step 4b: + = a
Which best explains or justifies Step 4b?

answer

converting to a common denominator

question

Anderson uses the discriminant to correctly find the number of real solutions of the quadratic equation x2 + 4x + 8 = 0. Which explanation could Anderson provide?

answer

The equation has one real number solution because the discriminant is 0

question

Rhett is solving the quadratic equation 0= x2 - 2x - 3 using the quadratic formula. Which shows the correct substitution of the values a, b, and c into the quadratic formula?

answer

D.

question

Zacharias is using the quadratic formula to solve the equation 0 = -2x2 + 5x - 3. He begins by substituting as shown.
Quadratic formula: x =
Substitution: x =
What error did Zacharias make?

answer

not a

question

Ramiya is using the quadratic formula to solve a quadratic equation. Her equation is x = after substituting the values of a, b, and c into the formula. Which is Ramiya's quadratic equation?
Quadratic formula: x =

answer

0 = x2 + 3x + 2

question

What is the discriminant of the quadratic equation 3 - 4x = -6x2?

answer

not a

question

Quincy uses the quadratic formula to solve for the values of x in a quadratic equation. He finds the solution, in simplest radical form, to be x = .
Which best describes how many real number solutions the equation has?

answer

not b or c

question

In simplest radical form, what are the solutions to the quadratic equation 6 = x2 - 10x?
Quadratic formula: x =

answer

not c

question

What is the discriminant of the quadratic equation 0 = 2x2 + 3x - 5?

answer

not c

question

What are the zeros of the function f(x) = x2 + 5x + 5 written in simplest radical form?
Quadratic formula: x =

answer

c

question

A quadratic equation of the form 0 = ax2 + bx + c has a discriminant value of 0. How many real number solutions does the equation have?

answer

1

question

A quadratic equation has a discriminant of 12. Which could be the equation?

answer

0 = 2x2 + 6x + 3

question

Nathaniel is using the quadratic formula to solve 0 = x2 + 5x - 6. His steps are shown below.
What are the solutions to the equation?

answer

x = -6, 1

question

A quadratic equation has exactly one real number solution. Which is the value of its discriminant?

answer

not c or d

question

In simplest radical form, what are the solutions to the quadratic equation 0 = -3x2 - 4x + 5?
Quadratic formula: x =

answer

not b

question

What is the discriminant of the quadratic equation 0 = -x2 + 4x - 2?

answer

8

question

What is the discriminant of the quadratic equation 0 = 2x2 + 3x - 5?

answer

not b or c

question

A quadratic equation of the form 0 = ax2 + bx + c has a discriminant value of -16. How many real number solutions does the equation have?

answer

not 2 or 1

question

What is the positive solution to the equation 0 = -x2 + 2x + 1?
Quadratic formula: x =

answer

not b

question

What is the value of the discriminant of the quadratic equation β1 = 5x2 β2x, and what does its value mean about the number of real number solutions the equation has?

answer

not c

question

Mattie uses the discriminant to determine the number of zeros the quadratic equation 0 = 3x2 - 7x + 4 has. Which best describes the discriminant and the number of zeros?

answer

The equation has two zeros because the discriminant is greater than 0.

question

Which function has real zeros at x = β10 and x = β6?

answer

f(x) = x2 + 16x + 60

question

What are the solutions to the quadratic equation 4(x + 2)2 = 36

answer

x = β5 and x = 1

question

Solve x2 + 6x = 7 by completing the square. Which is the solution set of the equation?

answer

{-7, 1}

question

What is a solution to (x + 6)(x + 2) = 60?

answer

x = 4

question

What are the zeros of the quadratic function f(x) = 2x2 + 8x - 3?

answer

A.

question

Two numbers are 10 units away in different directions from their midpoint, m, on a number line. The product of the numbers is -99.
Which equation can be used to find m, the midpoint of the two numbers?

answer

m2 - 100 = -99

question

Mariya is solving the quadratic equation by completing the square.
4x2 - 20x + 3 = 0
4x2 - 20x = -3
A(x2 - 5x) = -3
What is the value of A?

answer

4

question

Mischa wrote the quadratic equation 0 = -x2 + 4x - 7 in standard form. What is the value of c in her equation?

answer

-7

question

Liliana decides to crop a square photo 2 inches on each side to fit it into a frame. The area of the original photo was 121 square inches. In the equation (x + 2)2 = 121, x represents the side measure of the cropped photo.
What are the dimensions of the cropped photo?

answer

9 inches by 9 inches

question

Which is the graph of a quadratic equation that has a negative discriminant?

answer

D.

question

Heather is writing a quadratic function that represents a parabola that touches but does not cross the x-axis at x = -6. Which function could Heather be writing?

answer

f(x) = -x2 - 12x - 36

question

The first step in solving the quadratic equation -5x2 + 8 = 133 is to subtract from each side.

answer

8

question

The first few steps in solving the quadratic equation 5x2 + 27x = 14 β 13x by completing the square are shown.
5x2 + 27x = 14 β 13x
5x2 + 40x = 14
5(x2 + 8x) = 14
Which is the best step to do next to solve the equation by completing the square?

answer

5(x2 + 8x + 16) = 94

question

Which is a solution to the equation?
(x β 3)(x β 5) = 35

answer

x = 10

question

Solve x2 β 24x = β80 by completing the square.
What is the solution set of the equation?

answer

{4, 20}

question

What is the value of the discriminant of the quadratic equation β2x2 = β8x + 8, and what does its value mean about the number of real number solutions the equation has?

answer

The discriminant is equal to 0, which means the equation has one real number solution.

question

The function g(x) is defined as g(x) = 6x2 + 23x - 4. When does g(x) = 0?

answer

B.

question

Solve x2 - 8x = 20 by completing the square. Which is the solution set of the equation?

answer

{-2, 10}

question

What are the solutions to m2 - 9 = 0?

answer

m = -3 and m = 3

question

A quadratic equation of the form 0 = ax2 + bx + c has one real number solution. Which could be the equation?

answer

0 = -2x2 - 4x - 2

question

Heather is writing a quadratic function that represents a parabola that touches but does not cross the x-axis at x = -6. Which function could Heather be writing?

answer

f(x) = -x2 - 12x - 36

question

A quadratic equation has zero real number solutions. Which could be the discriminant value associated with this equation?

answer

-5

question

Between which two ordered pairs does the graph of f(x) = x2 + x - 9 cross the negative x-axis?
Quadratic formula: x =

answer

(-6, 0) and (-5, 0)

question

Sergey is solving 5x2 + 20x - 7 = 0. Which steps could he use to solve the quadratic equation? Check all that apply.

answer

2,3,and4

question

What is the value of the discriminant, b2 β 4ac, for the quadratic equation 0 = β2x2 β 3x + 8, and what does it mean about the number of real solutions the equation has?

answer

The discriminant is 73, so the equation has 2 real solutions.