Question

What is the vertex of the function f(x) = 1/2x2 + 3x + 3/2?

Answer 1

(-3,-3) just took the test on edg

Explanation:

Answer 2

vertex of the function is
`(-3,-3)`

Explanation:

Given Function, f(x) =
`(1)/(2)x^2+3x+(3)/(2)`

Simplify the given function to find the vertex.

use completing the square method.

`f(x)=(1)/(2)x^2+3x+(3)/(2)`

`f(x)=(1)/(2)(x^2+6x+3)`

`f(x)=(1)/(2)(x^2+6x+9-9+3)`

`f(x)=(1)/(2)((x^2+6x+9)-9+3)`

`f(x)=(1)/(2)((x+3)^2-6)`

`f(x)=(1)/(2)(x+3)^2-3`

let
`y=(1)/(2)(x+3)^2-3`

`2(y+3)=(x+3)^2`

`(x+3)^2=2(y+3)`

Therefore, vertex of the function is
`(-3,-3)`