Question

Question #08c9e

Answer 1

`f(x)=5(x-3/5)^2+11/5`

Explanation:

Given the following function,

`f(x)=5x^2-6x+4`

Factor the `a` value from the first two terms.

`f(x)=5(x^2-6/5x)+4`

Use `c=(b/2)^2` to find the `c` term in order to let `x^2-6/5x` be a trinomial.

`f(x)=5(x^2` `color(red)(-6/5)x+((color(red)(-6/5))/2)^2)+4`

Subtract `((-6/5)/2)^2` from the added `((-6/5)/2)^2`.

`f(x)=5(x^2color(red)(-6/5)x+((color(red)(-6/5))/2)^2-((color(red)(-6/5))/2)^2)+4`

Simplify.

`f(x)=color(blue)5(x^2-6/5x+9/25` `color(purple)(-9/25))+4`

Multiply `-9/25` by `5` to bring the `-9/25` out of the brackets.

`f(x)=color(blue)5(x^2-6/5x+9/25)+4+color(blue)5(color(purple)(-9/25))`

`color(green)(|bar(ul(color(white)(a/a)color(black)(f(x)=5(x-3/5)^2+11/5)color(white)(a/a)|)))`