Question

How do you write `f(x)= 3x^2-24x+45` in vertex form?

Answer 1

Given `f(x) = 3x^2-24x+45`

Vertex form is
`color(white)("XXXX")` `f(x) = (x-a)^2 +b` with the vertex at `(a, b)`

`f(x) = 3x^2-24x+45`
`color(white)("XXXX")` `f(x) = 3(x^2-8x) +45` `color(white)("XXXX")`extracting the `m`

`color(white)("XXXX")` `f(x) = 3(x^2-8x+16) + 45 - 3(16)` `color(white)("XXXX")`completing the square

`color(white)("XXXX")` `f(x) = 3(x-4)^2 -3` `color(white)("XXXX")`vertex form