Solving Quadratic Equations: Completing the Square — Unit test Answers

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

An architect designs a diagonal path across a rectangular patio. The path is 29 meters long. The width of the patio is x meters, and the length of the path is 5 meters more than the width.

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

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

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?

The product of two consecutive integers is 272. Which quadratic equation can be used to find x, the smaller number?

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?

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

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

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

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?

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

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

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