Solving Quadratic Equations Unit Test 100%

The function g(x) = x^2 - 10x + 24 is graphed on a coordinate plane. Where will the function cross the x-axis?

(4, 0) and (6, 0)

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

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

The product of two consecutive integers is 420. An equation is written in standard form to solve for the smaller integer by factoring. What is the constant of the quadratic expression in this equation? x^2 + x + _____ = 0

-420

Which are the solutions of x^2 = -5x + 8?

-5 - √57/2, -5 + √57/2

Brianna is graphing the function f(x) = x^2 + 6x + 5. What x-intercepts should Brianna use to graph f(x)?

-5 and -1

Nina knows that the average of the x-intercepts represents the line of symmetry for a quadratic function through the x-axis. Which equation represents the average of the x-intercepts for f(x) = 4x^2 - 24x + 20?

1 + 5/2 = 3

What value of c makes x^2 − 24x + c a perfect square trinomial?

144

What number should be added to both sides of the equation to complete the square? x^2 + 8x = 4

16

The roots of the function f(x) = x^2 - 2x - 3 are shown. What is the missing number? x = -1 and x =

3

What number should be added to both sides of the equation to complete the square? x^2 + 12x = 11

36

What value of c makes x^2 − 12x + c a perfect square trinomial?

36

Which are the solutions of the quadratic equation? x^2 = 9x + 6

9 - √105/2, 9 + √105/2

What values of b satisfy 3(2b + 3)^2 = 36?

b = -3+2↓13/2 and -3 - 2 √3/2

Which are the roots of the quadratic function f(b) = b^2 - 75? Check all that apply.

b = 5√3 b = -5√3

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

f(x) = x^2 - 12x + 20

Two positive integers are 3 units apart on a number line. Their product is 108. Which equation can be used to solve for m, the greater integer?

m(m - 3) = 108

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?

w(w + 2) = 48

What are the solutions to the equation 0 = x^2 - x - 6? Check all that apply.

x = -2 x = 3

What are the solutions to x^2 + 8x + 7 = 0?

x = -7 and x = -1

What are the solution(s) to the quadratic equation 40 − x^2 = 0?

x = ±2√10

What are the solution(s) to the quadratic equation 50 - x^2 = 0?

x = ±5√2

Two negative integers are 8 units apart on the number line and have a product of 308. Which equation could be used to determine x, the smaller negative integer?

x^2 + 8x - 308 = 0

A square picture with a side length of 4 inches needs to be enlarged. The final area needs to be 81 square inches. Which equation can be used to solve for x, the increase in side length of the square in inches?

x^2 + 8x - 65 = 0

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

x^2 - 4 = 0 4x^2 = 16

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? Check all that apply.

y^2 - 5y = 750 750 - y(y - 5) = 0 (y + 25)(y - 30) = 0