Review for Complete the Square and Quadratic Formula

Front

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

Back

Subtract 21 from both sides.

Front

What are the solutions to the equation 2x² + 2x - 12 using the quadratic formula?

Back

x = 2, x = -3

Front

Solve the equation n² - 2n - 3 = 0 by completing the square.

Back

n = 3, n = -1

Front

Write the quadratic expression x² + 8x - 1 in completed square form.

Back

(x + 4)² - 17

Front

When factoring x² - 4x + 4 = 20, what goes in the blank? (x - __ )² = 20

Back

2

Front

What is the quadratic formula?

Back

x = (-b ± √(b² - 4ac)) / (2a)

Front

What does completing the square involve?

Back

Rewriting a quadratic in the form (x - p)² = q.

Front

How do you find the vertex of a parabola given in standard form y = ax² + bx + c?

Back

The vertex is at x = -b/(2a).

Front

What is the discriminant in the quadratic formula?

Back

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

Front

What does it mean if the discriminant is positive?

Back

There are two distinct real roots.