Completing the Square Practice

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be expressed as the square of a binomial. It takes the form (a ± b)² = a² ± 2ab + b².

Front

Identify the perfect square trinomial from the expression: x² - 18x + 81.

Back

(x - 9)²

Front

Identify the perfect square trinomial from the expression: x² + 14x + 49.

Back

(x + 7)²

Front

What value of 'c' makes the expression x² - 8x + c a perfect square trinomial?

Back

16

Front

Complete the square for the expression: x² - 14x + ___.

Back

49

Front

What is the first step in completing the square for the equation y² + 10y = -9?

Back

Move the constant to the other side: y² + 10y + ___ = -9 + ___.

Front

What is the formula for completing the square?

Back

To complete the square for ax² + bx + c, rewrite it as a(x + b/2a)² - (b² - 4ac)/4a.

Front

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

Back

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

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

Solve by completing the square: y² + 10y = -9. What are the solutions?

Back

The solutions are y = -1 and y = -9.