Question

The first steps in writing f(x) = 4x^2 + 48x + 10 in vertex form are shown.

f(x) = 4(x2 + 12x) + 10

What is the function written in vertex form?

Answer 1

f(x) = 4x^2 + 48x + 10
f(x) = 4(x^2 + 12x) + 10
f(x) = 4(x^2 + 12x + 36) + 10
f(x) = 4(x + 6)^2 + 10

Answer 2

The vertex from of the given function is
`f(x)=4(x+6)^2-134`.

Explanation:

The given function is

`f(x)=4x^2+48x+10`

`f(x)=4(x^2+12x)+10`

If a expression is given as x²+bx, then add
`((b)/(2))^2` in the expression to make it perfect square.

Here b=12, so add and subtract
`((12)/(2))^2` in the parentheses.

`f(x)=4(x^2+12x+6^2-6^2)+10`

`f(x)=4(x^2+12x+6^2)+4(-6^2)+10`

`f(x)=4(x+6)^2-4(36)+10`

`f(x)=4(x+6)^2-144+10`

`f(x)=4(x+6)^2-134`

Therefore the vertex from of the given function is
`f(x)=4(x+6)^2-134`.