Question

What is the vertex form of `y= (9x-6)(3x+12)-7x^2+5x`?

Answer 1

`y = 20(x-(-19/8))^2-2957/16`

Explanation:

Given: `y= (9x-6)(3x+12)-7x^2+5x`

Perform the multiplication:

`y =27x^2 + 90x - 72 -7x^2+5x`

Combine like terms:

`y =20x^2 + 95x - 72`

This is in the standard Cartesian form:

`y = ax^2+bx+c`

where `a = 20, b = 95, and c = -72`

The general vertex form for a parabola of this type is:

`y = a(x-h)^2+k`

We know that `a = 20`:

`y = 20(x-h)^2+k`

We know that `h = -b/(2a)`

`h = -95/(2(20))`

`h = -19/8`

`y = 20(x-(-19/8))^2+k`

We know that:

`k = 20(-19/8)^2+95(-19/8)-72`

`k = -2957/16`

`y = 20(x-(-19/8))^2-2957/16`