Factoring Quadratic Equations

Front

True or false: The solution, root, x-intercept, and zero of a problem are all the same thing.

Back

True

Front

What are the solutions to this equation? (x-3)(x+2)=0

Back

x=3, -2

Front

What are the x-intercepts for the following: (2x - 2)(5x + 5) = 0

Back

x = -1 or x = 1

Front

What should you do first in solving this equation? x² + 6x - 13 = 3

Back

Make it equal 0 by subtracting 3 on each side

Front

Factor: 2x² + 13x + 15

Back

(2x + 3)(x + 5)

Front

What is a quadratic equation?

Back

An equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to factor a quadratic equation?

Back

To express the quadratic equation as a product of its linear factors.

Front

What is the quadratic formula?

Back

x = (-b ± √(b² - 4ac)) / (2a) for ax² + bx + c = 0.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: two real and distinct, one real and repeated, or two complex.

Front

How do you find the x-intercepts of a quadratic equation?

Back

Set the equation equal to zero and solve for x.