Solving Quadratics (All methods)

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 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 roots 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 (the product of a and c) and add to b (the coefficient of x).

Front

What does it mean to complete the square?

Back

Completing the square involves rewriting a quadratic equation in the form (x - p)² = q, making it easier to solve.

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero.

Front

How do you solve x² + 10x = -9?

Back

Rearrange to x² + 10x + 9 = 0, then factor to (x + 1)(x + 9) = 0, giving roots x = -1 and x = -9.

Front

What is the solution to 3x² - 6x - 24 = 0?

Back

Factor to 3(x + 2)(x - 4) = 0, giving roots x = -2 and x = 4.

Front

How do you use the quadratic formula to solve 7x² - 26x - 8 = 0?

Back

Using the quadratic formula, x = (26 ± √(26² - 4*7*(-8))) / (2*7), resulting in x = 4 and x = -2/7.

Front

What is the solution to (x + 1)² = 25?

Back

Taking square roots gives x + 1 = ±5, leading to solutions x = 4 and x = -6.