Complete the Square

Front

What is the process to complete the square for a quadratic equation?

Back

1. Move the constant term to the other side of the equation. 2. Take half of the coefficient of x (the b value), square it, and add it to both sides. 3. Factor the left side as a perfect square.

Front

What do you do to the b value to correctly complete the square?

Back

Divide it by 2 and square the result.

Front

What value of c would make this a perfect square trinomial? x² - 12x + c

Back

36

Front

Is this a perfect square trinomial? x² + 18x + 9

Back

No

Front

What value of c would make this a perfect square trinomial? x² + 8x + c

Back

16

Front

Factor the perfect square trinomial x² + 14x + 49

Back

(x + 7)²

Front

What is a perfect square trinomial?

Back

A trinomial that can be expressed as the square of a binomial, in the form (a + b)² or (a - b)².

Front

How do you identify a perfect square trinomial?

Back

Check if the first and last terms are perfect squares and if the middle term is twice the product of the square roots of the first and last terms.

Front

What is the formula for completing the square?

Back

For a quadratic ax² + bx + c, the completed square form is a(x + b/2a)² - (b² - 4ac)/4a.

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.