5.2.2 Complete the Square jut c

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, typically in the form (a + b)² = a² + 2ab + b².

Front

How do you factor the perfect square trinomial x² + 14x + 49?

Back

The expression factors to (x + 7)².

Front

What value of c makes the expression x² - 12x + c a perfect square trinomial?

Back

The value of c is 36.

Front

What is the first step in completing the square for the expression x² + 10x?

Back

Divide the b value (10) by 2, which gives 5.

Front

What do you do with the result after dividing the b value by 2 when completing the square?

Back

Square the result. In this case, 5² = 25.

Front

Complete the square for the expression x² + 12x + ___. What is the missing number?

Back

The missing number is 36, so the complete expression is x² + 12x + 36.

Front

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

Back

The formula is x = -b/(2a) to find the vertex, and then use (x + b/2)² - (b² - 4ac)/4a.

Front

How do you determine the value of c in the expression x² - 8x + c to make it a perfect square trinomial?

Back

Take half of -8 (which is -4), square it to get 16. Thus, c = 16.

Front

What is the general form of a perfect square trinomial?

Back

The general form is (x + p)² = x² + 2px + p².

Front

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

Back

Completing the square allows you to rewrite a quadratic equation in vertex form, making it easier to analyze and solve.