Question

Write the quadratic function f(x) = x^2 + 8x + 3 in vertex form?

A) f(x) = (x - 4)^2 - 13

B) f(x) = (x - 4)^2 + 3

C) f(x) = (x + 4)^2 + 3

D) f(x) = (x + 4)^2 - 13

Answer 1

you have to complete the square.

Explanation:

`x^2+8x+3`

first you have to open a bracket and put the `x`
into it add up to half of the term b which is `8x` and square it.

`(x+(8x)/2)^2`

`(x+4x)^2`

always completing the square, the sign after the brackets is negative. Then you have to half again the term b and square it.

`(x+4x)^2-4^2`

And finally you have to add the term c which is 3 in this case.
`(x+4x)^2-4^2+3`

Simplify
`(x+4x)^2-16-3`

Answer
`(x+4x)^2-13`

vertex is (-4,-13)