Question

Which equation is y=9x^2+9x-1 re-written in vertex form

Answer 1

A. y = 9(x +1/2)^2 - 13/4.

Explanation:

y = 9x^2 + 9x - 1

y = 9(x^2 + x) - 1

y = 9 [ (x + 1/2)^2 - 1/4] - 1

y = 9 (x + 1/2)^2 - 9/4 - 1

y = 9(x +1/2)^2 - 13/4.

Answer 2

Answer: First Option

`y = (x+(1)/(2)) ^ 2 -(13)/(4)[`

Explanation:

For a quadratic function of the form:

`y = ax ^ 2 + bx + c`

The vertex form of the equation is:

`y = (x-h) ^ 2 + k`

Where the vertex is the point (h, k) and
`h =-(b)/(2a)`

In this case the equation is:
`y=9x^2+9x-1`

So:

`a=9\\b=9\\c=-1`

Therefore:

`h =-(9)/(2*(9))`

`h =-(1)/(2)`

`k=9(-(1)/(2))^2+9(-(1)/(2))-1\\\\k=-(13)/(4)`

Finally the equation in vertex form is:

`y = (x+(1)/(2)) ^ 2 -(13)/(4)[`