Quadratic Equations Unit Test Review

The first three steps in determining the solution set of the system of equations algebraically are shown in the table. y = −x2 +2x − 9y = −6x + 6 What are the solutions of this system of equations?

A) (5, −24) and (3, −12)

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

A) -5

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

A) 0 = -2x2 + x + 3

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

A) b = and b = -2

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

A) f(x) = x2 + 16x + 60

What is the value of the discriminant of the quadratic equation −2x2 = −8x + 8, and what does its value mean about the number of real number solutions the equation has?

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

The first two steps in determining the solution set of the system of equations, y = -x2 + 4x + 12 and y = -3x + 24, algebraically are shown in the table. Which represents the solution(s) of this system of equations?

C) (3, 15) and (4, 12)

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

C) 0 = -2x2 - 4x - 2

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

C) x = 4

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

C) x = −5 and x = 1

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?

D) 28

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?

D) m2 - 100 = -99

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

D) x = 10

Which steps could be part of the process in algebraically solving the system of equations, y + 5x = x2 + 10 and y = 4x - 10? Select two options.

D, E

Which graph shows a system of equations with a solution at (2, -1)?

Graph D