Question

Use the process of completing the square to fill in the blanks.

y = x2 + 8x + 25

Answer 1

16: y = (x^2 + 8x + 16) + 25 - 16

Explanation:

To complete the square use (b/2)^2.

Before completing the square, make sure that the a-value is 0. This means that there can be no coefficient to x^2. If there is then factor out this coefficient.

The b-value in this quadratic equation, y = x^2 + 8x + 25, is the coefficient of x. Therefore it is 8. Substitute 8 into the formula to complete the square.

• ((8))/2)^2

Start by solving inside the parentheses. Divide 8 by 2.

• (4)^2

Evaluate the exponent.

• 16

Separate the c-value from the a and b values with parentheses like so:

y = (x^2 + 8x) + 25

The blanks should be in the parentheses and outside of the parentheses like so:

y = (x^2 + 8x + __) + 25 - __

You add the answer that you got from (b/2)^2 inside the parentheses and subtract it from the outside of the parentheses.

The number that should fill in the blanks is 16.

y = (x^2 + 8x + 16) + 25 - 16