ALG Unit 4C Review - Solving Quadratic Equations (ALL Methods)

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 are the methods to solve quadratic equations?

Back

The methods to solve quadratic equations include factoring, using the quadratic formula, completing the square, and graphing.

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

How do you factor a quadratic equation?

Back

To factor a quadratic equation, find two numbers that multiply to ac and add to b, then rewrite the equation as (px + q)(rx + s) = 0.

Front

What does the discriminant tell you?

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: 16a² - 9 = 0

Back

a = -3/4, 3/4

Front

Solve using the quadratic formula: x² - 3x - 4 = 0

Back

x = 4 and -1

Front

Use the quadratic formula to find the solutions for: 0 = -x² - 5x + 12

Back

x = -6.77 and 1.77

Front

Solve by completing the square: k² − 12k + 23 = 0

Back

k = 6 + √13, 6 - √13

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.