Lesson 10.2 Completing the Square

Front

Complete the square for the expression: x² + 14x + ____

Back

x² + 14x + 49

Front

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

Back

(x + 3)² = 14

Front

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

Back

x = 4, -10

Front

Complete the square for the expression: x² + 6x + ____

Back

x² + 6x + 9

Front

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

Back

2

Front

What is the process of completing the square?

Back

Completing the square involves rewriting a quadratic equation in the form (x - p)² = q, where p and q are constants.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

How do you find the vertex of a parabola from the standard form?

Back

The vertex can be found using the formula h = -b/(2a) and k = f(h) for the quadratic ax² + bx + c.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

What is the standard form of a quadratic equation?

Back

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