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 in factored form?

Back

To find the roots of a quadratic equation in factored form (x - p)(x - q) = 0, set each factor equal to zero: x - p = 0 and x - q = 0, then solve for x.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of any 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 > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

Solve: 3x² - 192 = 0

Back

x = -8 or 8.

Front

Solve: x² + 44 = -15x

Back

x = -11 or -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

The zeros are x = -10 and x = 2.

Front

Solve: a² + 2a - 24 = 0

Back

a = -6 or 4.