Solving Quadratics by Factoring

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to solve a quadratic equation by factoring?

Back

Solving a quadratic equation by factoring involves rewriting the equation in the form (px + q)(rx + s) = 0 and then finding the values of x that make each factor equal to zero.

Front

What are the 'zeros' of a quadratic function?

Back

The 'zeros' of a quadratic function are the x-values where the graph intersects the x-axis, also known as the x-intercepts.

Front

How do you find the zeros of a quadratic equation?

Back

To find the zeros, set the quadratic equation equal to zero and solve for x, either by factoring, using the quadratic formula, or completing the square.

Front

What is the first step in factoring a quadratic equation?

Back

The first step in factoring a quadratic equation is to look for a greatest common factor (GCF) among the terms.

Front

Solve by factoring: x² - 5x + 6 = 0

Back

x = 2 and x = 3.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation.

Front

Solve by factoring: 2x² + 8x = 0

Back

x = 0 and x = -4.

Front

What does the discriminant tell you about a quadratic equation?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

Solve by factoring: x² - 9 = 0

Back

x = 3 and x = -3.