Question

How do you write the Vertex form equation of the parabola `y=x^2 - 9x`?

Answer 1

The vertex form is `(x-4.5)^2+20.25`.

Explanation:

`y=x^2-9x` is the standard form for a parabola: `ax^2+bx+c`, where `a=1`, `b=-9`, and `c=0`.

The vertex form is `y=a(x-h)^2+k`, where `h=(-b)/(2a)` and `k=f(h)`

`h=(-(-9))/(2*1)=4.5`

Substitute the value of `h` for `x` into the standard form.

`k=f(h)=(4.5)^2-9(4.5)=-20.25`

Vertex form is `(x-4.5)^2+20.25`