Completing the square.

Front

What is the first step in completing the square for a quadratic equation?

Back

Rearrange the equation to isolate the constant term on one side.

Front

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

Back

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

Front

What is the formula for completing the square for the quadratic expression ax^2 + bx + c?

Back

The completed square form is a(x + b/2a)^2 - (b^2 - 4ac)/4a.

Front

What does a perfect square trinomial look like?

Back

It can be expressed in the form (x - p)^2 or (x + p)^2.

Front

What is the relationship between the coefficients in a perfect square trinomial?

Back

The middle term is twice the square root of the constant term.

Front

Given the expression x^2 - 14x, what value must be added to complete the square?

Back

49, because (-14/2)^2 = 49.

Front

How do you convert the expression x^2 - 10x + 25 into its factored form?

Back

It can be factored as (x - 5)^2.

Front

What is the missing value 'c' in the expression x^2 + 26x + c to make it a perfect square trinomial?

Back

169, because (26/2)^2 = 169.

Front

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

Back

It allows for easier identification of the vertex and helps in graphing the parabola.

Front

How can completing the square be used to derive the quadratic formula?

Back

By rearranging the standard form of a quadratic equation and completing the square.