Question

How do you find the equation of a parabola when given a vertex (3, -3) point (0, 6)?

Answer 1

I found: `y=x^2-6x+6`

Explanation:

You have
1] the general equation of your parabola:
`y=ax^2+bx+c " " (1)`
2] two points of your parabola:

`x=3, y=-3` which is also the vertex. At the vertex `x_v=3=-b/(2a)`;

`x=0, y=6`

we can try use these information into equation (1):

`-3=9a+3b+c`

`6=0a+0b+c` so that `color(red)(c=6)`

`3=-b/(2a)` and `b=-6a`

So we can get, from the first (with `c=6` and `b=-6a`):
`-3=9a-18a+6` and `color(red)(a=1)`
and so: `b=-6a=color(red)(-6)`

The equation of the parabola is:
`y=x^2-6x+6`
Graphically:
graph{x^2-6x+6 [-16.02, 16.02, -8.01, 8.01]}