Quadratic Equations

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

-7

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

0 = -2x2 + x + 3

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

8

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.

9 inches by 9 inches

What are the solutions to m2 - 9 = 0?

m = -3 and m = 3

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

m2 - 100 = -99

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

x=4

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?

28

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

D

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 73, so the equation has 2 real solutions.

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

b =2/3 and b = -2

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 - 12x - 36

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

f(x) = x2 + 16x + 60

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

x = -4 or x = 1/6

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

x = −5 and x = 1