Solving Quadratics - 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: 2x² + 7x - 15 = 0

Back

x = -5 or x = 1.5

Front

Solve: 3a² - 12a + 12 = 0

Back

a = 2

Front

Solve: 9k² = 225

Back

k = -5 or k = 5

Front

What are the x-intercepts of the graph of a quadratic equation?

Back

The x-intercepts are the points where the graph intersects the x-axis, corresponding to the solutions of the quadratic equation.

Front

Solve: 4m² - 100 = 0

Back

m = 5 or m = -5