Completing the Square

Front

What is completing the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting them in the form of a perfect square trinomial, allowing for easier solutions.

Front

What is the first step to solving the equation a^2 + 10a + 21 = 0 by completing the square?

Back

Subtract 21 from both sides.

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 or (x - a)^2.

Front

Identify the equivalent expression for the perfect square trinomial x^2 + 14x + 49.

Back

(x + 7)^2.

Front

How do you find the value to complete the square for the expression x^2 + bx?

Back

Take half of b, square it, and add it to both sides of the equation.

Front

What is the formula for completing the square for the quadratic equation ax^2 + bx + c = 0?

Back

Rearrange to x^2 + (b/a)x = -c/a, then complete the square.

Front

Solve the equation x^2 - 6x - 27 = 0 by completing the square.

Back

x = {-3, 9}.

Front

Identify the equivalent expression for the perfect square trinomial x^2 - 18x + 81.

Back

(x - 9)^2.

Front

Is x^2 + 18x + 9 a perfect square trinomial?

Back

No.

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.