Solving Quadratic Equations by Completing the Square

Front

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

Back

True

Front

What is the first step to solving the equation a² + 10a + 21 = 0 by completing the square?

Back

Subtract the 21.

Front

What is the first step to solving the equation 2a² + 10a = -12 by completing the square?

Back

Divide both sides by 2.

Front

Solve by completing the square: x² − 10x - 11 = 0

Back

x = −1 and 11.

Front

When factoring x² - 4x = 16, what goes in the blank? (x __ )² = 16

Back

-2.

Front

What is a quadratic equation?

Back

An equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to complete the square?

Back

To transform a quadratic equation into a perfect square trinomial, making it easier to solve.

Front

What is the vertex form of a quadratic equation?

Back

y = a(x - h)² + k, where (h, k) is the vertex.

Front

How do you find the vertex of a quadratic equation in standard form?

Back

Use the formula h = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is b² - 4ac, which determines the nature of the roots.