Completing the square.

Front

What is the process of completing the square?

Back

Completing the square is a method used to convert a quadratic equation into a perfect square trinomial, making it easier to solve or analyze.

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 + a)² = x² + 2ax + a².

Front

How do you find the value to complete the square for x² - 10x?

Back

Take half of the coefficient of x (which is -10), square it (25), and add it to the expression: x² - 10x + 25.

Front

What is the value needed to complete the square for x² - 14x?

Back

The value is 49, since (-14/2)² = 49.

Front

Complete the square for x² + 6x + ___.

Back

The missing value is 9, because (6/2)² = 9.

Front

Find the missing value 'c' for x² + 26x + ___.

Back

The missing value is 169, since (26/2)² = 169.

Front

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

Back

The formula is x = -b/(2a) ± √(b² - 4ac)/(2a).

Front

How do you convert x² - 12x into a perfect square?

Back

Add (12/2)² = 36 to get x² - 12x + 36.

Front

What is the significance of completing the square in solving quadratic equations?

Back

It allows for easier graphing, finding vertex form, and solving equations by isolating the variable.

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.