Question

What is the vertex form of `y= 3x^2-30x-72`?

Answer 1

`y=3(x-5)^2 -147`

Explanation:

Given:`" "y=3x^2-30x-72`

Let `k` be the correction canstant

Write as;`" "y=3(x^(color(magenta)(2))-30/3x)-72+k`

Move the power of `color(magenta)(2)` to outside the bracket

`y=3(x-30/3color(green)(x))^(color(magenta)(2))-72+k`

Remove the `color(green)(x)` from `30/3x`

`y=3(x-30/3)^2 -72+k`

Apply `1/2xx(-30/3) = 30/6 = 5`

`y=3(x-5)^2 -72+k`

For the correction to work it has to be the case that

`color(red)(3)xx(-5)^2+k=0" "=>" "k=-75`

`color(red)("(do not forget to multiply by the value outside the brackets)")`

`y=3(x-5)^2 -72-75`

`y=3(x-5)^2 -147`