Write the quadratic in standard form

Question

Write the quadratic function in standard form.

g(x) = x² + 8x + 16

Answer 1

First they are asking if you know what "standard form" for quadratic equations is. It is

So given g(x) = x² + 8x + 16, you will note you will need to complete the square to get it into the standard form.

1. to complete the square, you take 1/2 the value of "B" (Ax² +Bx + C) and square it.
2. (x+4)² +16
3. Then you will need to "undo" the effect of the last term multiplied by itself (so you will need to "undo" or negate, (4)(4), to negate subtract 16
4. (x+4)² +16 - 16 (by the way, it is purely coincidence that the +16 in the original equation given is the same number that you will need to "undo" the last term effect in completing the square.)
5. So... g(x) = (x+4)² is your answer. Or g(x) = 1(x+4)² + 0 (same thing)

Answer 2

My answer is the expression is a perfect square. So we can write it as (x+4)^2.