4.9: Solving Quadratics by Completing the Square/Square Root

Front

What is the process of completing the square in a quadratic equation?

Back

Completing the square involves rewriting a quadratic equation in the form (x - p)² = q, where p and q are constants. This method helps in solving the equation by making it easier to find the roots.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you find the vertex of a parabola given by the equation y = ax² + bx + c?

Back

The vertex can be found using the formula x = -b/(2a). The y-coordinate can be found by substituting this x value back into the equation.

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant, given by b² - 4ac, indicates the nature of the roots: if it's positive, there are two distinct real roots; if zero, there is one real root; if negative, there are two complex roots.

Front

Solve the quadratic equation by completing the square: x² + 4x + 1 = 0.

Back

x = -2 ± √3.

Front

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

Back

n = 3 and n = -1.

Front

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

Back

2.

Front

Solve the equation by completing the square: x² + 6x - 4 = 36.

Back

x = 4 and x = -10.

Front

Complete the square for the equation x² + 6x = 5.

Back

(x + 3)² = 14.

Front

What is the first step in completing the square for the equation x² + bx?

Back

Divide the coefficient b by 2 and square the result.