Question

Complete the square to re-write the quadratic function in vertex form

Answer 1

`y= (x+(1)/(2))^2-8.25`

Explanation:

First, we move the c in
`ax^2+bx+c` to the other side of the equation by adding 8 onto both sides:

`x^2+x=8`.

Then, since
`x^2\\` has no coefficient, we make the left side a perfect square trinomial by adding
`((b)/(2))^2` on both sides of the equation. We do this because adding this to the equation will make the left side equal to
`(x\pm(b)/(2))^2` (plus-minus because the sign depends on if b is negative or positive):

`x^2+x+(1)/(4)=8+(1)/(4)`.

Then, simplify the left side:

`(x+(1)/(2))^2=8.25`

Finally, subtract 8.25 on both sides to make it vertex form:

`y= (x+(1)/(2))^2-8.25`