Completing the Square Practice

Front

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

Back

Completing the square involves rewriting a quadratic expression in the form (x - p)² + q, where p and q are constants. This helps in solving quadratic equations and converting them into vertex form.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

How do you find the missing number when completing the square for x² + 12x + ____?

Back

To find the missing number, take half of the coefficient of x (which is 12), square it (6² = 36), and add it to the expression: x² + 12x + 36.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, such as (x - p)² = x² - 2px + p².

Front

Convert the equation y = x² - 2x - 5 into vertex form.

Back

y = (x - 1)² - 6.

Front

Identify the equivalent expression for the perfect square trinomial x² - 18x + 81.

Back

(x - 9)².

Front

How do you convert f(x) = x² - 8x + 1 into vertex form?

Back

Complete the square: f(x) = (x - 4)² - 15.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the highest or lowest point of the parabola, depending on the direction it opens (upward or downward).

Front

Write the quadratic expression x² - 6x - 3 in completed square form.

Back

(x - 3)² - 12.

Front

What is the formula to complete the square for a quadratic expression ax² + bx + c?

Back

1. Divide by a (if a ≠ 1). 2. Take half of b, square it, and add/subtract it inside the expression.