Answers FL-1200700-Mathematics for College Algebra MISSolving Quadratic Equations: Quadratic Formula

Solving Quadratic Equations: Quadratic Formula — Unit test Answers

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Mariya is solving the quadratic equation by completing the square.4x2-20x+3=04x2-20x=-3A(x2-5x)=-3

-20

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Solve x2 − 24x = −80 by completing the square.What is the solution set of the equation?

{2, 40}

{4, 20}

{5, 16}

{8, 10}

Clara writes the equation (x – 13)(x + 8) = 196 to solve for the missing side length of a rectangle represented by the factor x + 8. What is the missing side length represented by x + 8 units of the rectangle?

Using the Completing the Square method, what are the zeros of the quadratic function f(x) = 2x2 + 8x – 3?

x = –2 – and x = –2 +

x = –2 – and x = –2 +

x = 2 – and x = 2 +

x = 2 – and x = 2 +

Two numbers are 10 units away in different directions from their midpoint, m, on a number line. The product of the numbers is –99.

(m – 5)(m + 5) = 99

(m – 10)(m + 10) = 99

m2 – 25 = –99

m2 – 100 = –99

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

{–22, 14}

{–14, 22}

{–10, 2}

{–2, 10}

Which equation has an a-value of –2, a b-value of 1, and a c-value of 3?

0 = –2x2 + x + 3

0 = 2x2 + x + 3

0 = –2x2 + 3

0 = 2x2 – x + 3

What values of b satisfy 4(3b + 2)2 = 64?

b = and b = –2

b = 2 and b =

b = and b = 3

b = 2 and b =

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

x = −8

x = −5

x = 2

x = 10

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

x = −6

x = −4

x = 4

x = 12

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?

f(x) = x2 + 36x + 12

f(x) = x2 – 36x – 12

f(x) = –x2 + 12x + 36

f(x) = –x2 – 12x – 36

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

x = –6 or x =

x = –4 or x =

x = or x = 6

x = or x = 4

What are the solutions to m2 – 9 = 0?

m = –9 and m = 0

m = –3 and m = 3

m = –3

m = 9

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

{–7, 1}

(negative 3 minus StartRoot 10 EndRoot comma negative 3 + StartRoot 10 EndRoot)

(3 minus StartRoot 10 EndRoot comma negative 3 + StartRoot 10 EndRoot)

{1, 7}

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.

8 inches by 8 inches

9 inches by 9 inches

12 inches by 12 inches

13 inches by 13 inches

A rectangle’s length is 5 inches more than twice its width. Its area is 50 square inches. Which equation can be used to find its width, w?

2w(2w + 5) = 50

2w(w + 5) = 50

w(2w + 5) = 50

w(w + 5) = 50

What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = −2x2 − 3x + 8, and what does it mean about the number of real solutions the equation has?

The discriminant is −55, so the equation has 2 real solutions.

The discriminant is −55, so the equation has no real solutions.

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

The discriminant is 73, so the equation has no real solutions.

Which function has real zeros at x = −10 and x = −6?

f(x) = x2 + 16x + 60

f(x) = x2 − 16x + 60

f(x) = x2 + 4x + 60

f(x) = x2 − 4x + 60

Two sandboxes with the same area are shown.The equation represents the area of Sandbox 2 in terms of its width.

2.72 meters

3.06 meters

9.16 meters

10.18 meters

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

0 = 2x2 – 4x + 1

0 = 2x2 – 5x + 3

0 = –2x2 – 4x – 2

0 = –2x2 – 3x – 1

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Solving Quadratic Equations: Quadratic Formula — Unit test Answers

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