Solving Quadratics

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 is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What is the Zero-Product Property?

Back

The Zero-Product Property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, express the quadratic in the form (x - p)(x - q) = 0, then set each factor to zero: x - p = 0 or x - q = 0.

Front

What is the quadratic formula?

Back

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

Front

What does the discriminant tell us?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

Solve: 4m² - 100 = 0

Back

m = 5, -5

Front

Solve: 2x² + 17x + 21 = 0

Back

x = -7, -3/2

Front

Solve using Zero-Product Property: (x-11)(5x+1) = 0

Back

x = 11 or x = -1/5

Front

Solve: a² + 2a - 24 = 0

Back

a = -6, 4