Solving Quadratics by Completing the Square Review

Front

What is the process of completing the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x + p)² = q, where p and q are constants.

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 complete the square for the equation x² + bx?

Back

To complete the square, take half of b, square it, and add it to both sides of the equation.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

Solve by completing the square: x² - 4x = 5.

Back

(x - 2)² = 9; x = 2 ± 3, so x = 5 or -1.

Front

What does it mean if the discriminant (b² - 4ac) is negative?

Back

If the discriminant is negative, the quadratic equation has no real solutions (the roots are complex).

Front

Solve by completing the square: x² + 6x + 8 = 0.

Back

(x + 3)² = 1; x = -3 ± 1, so x = -2 or -4.

Front

What is the formula for the vertex of a parabola given in standard form?

Back

The vertex (h, k) can be found using h = -b/(2a) and k = f(h), where f(x) is the quadratic function.

Front

Complete the square for the expression x² + 10x.

Back

(x + 5)² - 25.

Front

Solve by completing the square: x² + 4x - 5 = 0.

Back

(x + 2)² = 9; x = -2 ± 3, so x = 1 or -5.