Solving Quadratics

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What are the solutions of a quadratic equation called?

Back

The solutions of a quadratic equation are called roots, zeros, or x-intercepts.

Front

How do you find the roots of a quadratic equation using factoring?

Back

To find the roots using factoring, express the quadratic in the form (x - p)(x - q) = 0, where p and q are the roots.

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 of a quadratic equation tell us?

Back

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

Front

Solve: 4m² - 100 = 0

Back

m = 5, -5

Front

Solve: a² + 2a - 24 = 0

Back

a = -6, 4

Front

True or false: The solutions, roots, x-intercepts, and zeros of a quadratic equation are all the same thing.

Back

True

Front

Find the zeros of the equation: (x + 10)(x - 2) = 0

Back

-10 and 2

Front

Solve: x² + 44 = -15x

Back

{-11, -4