Complete the Square

Front

What is 'completing the square'?

Back

A method used to solve quadratic equations by rewriting them in the form (x - p)² = q.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants.

Front

How do you complete the square for the equation x² + bx?

Back

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

Front

What is the formula for the vertex of a parabola in the form y = ax² + bx + c?

Back

The vertex is at the point (-b/2a, f(-b/2a)).

Front

What is the first step in completing the square for the equation x² + 6x + 5 = 0?

Back

Subtract 5 from both sides to isolate the x² and x terms.

Front

If you have the equation x² + 4x = 12, what do you do next?

Back

Subtract 12 from both sides to get x² + 4x - 12 = 0.

Front

What do you do with the b value when completing the square?

Back

Divide it by 2 and square the result.

Front

What is the completed square form of x² + 8x?

Back

(x + 4)² - 16.

Front

How do you solve the equation (x + 3)² = 16?

Back

Take the square root of both sides: x + 3 = ±4, then solve for x.

Front

What is the solution to the equation x² - 10x + 25 = 0?

Back

x = 5, since it can be factored as (x - 5)² = 0.