Question

Question #54c16

Answer 1

Vertex `(h,k)=(3,-12)`

Explanation:

graph{x^2-6x-y-3=0 [-10.12, 9.88, -15.28, -5.28]}

If we are given quadratic in the form
`y = ax^2 + bx + c`, it represents a parabola.

You can complete the square to convert quadratic to vertex form, but, for finding the vertex, it's easier to use a formula.

The vertex `(h, k)` is found by computing `h = (–b)/(2a)`, then evaluating `y` at `h` to find `k`. Or from the formula: `k = (4ac – b^2) / (4a)`.
Observe similarity between discriminant of a quadratic and above formulae.
Given equation is
`x^2-6x-y-3=0`
Rewriting it in the given form
`y=x^2-6x-3`
`=>a=1, b=-6, c=-3`
`h=(–b)/(2a)`
`=>h=6/(2xx1)=3`
and `k = (4ac – b^2) / (4a)`
`k = (4xx1xx(-3) – (-6)^2) / (4xx1)`
`k = (-12 – 36) / 4=-12`