Question

How do you write the equation of each parabola in vertex form given vertex is (3,-6). and y intercept is 2?

Answer 1

The function is `y=8/9 x^2 - 16/3 x +2`

Any quadratic function can be written as `y=ax^2+bx+c` We know. that the function passes through point `(0,2)` so `c=2`.

The vertex of a parabola can be calculated using formula
`V=(p,q)` where `p=(-b)/(2a)`.

Third equation comes from the fact that the value of function `f(3)=-6`

So we know, that

1) `c=2`
2) `(-b)/(2a)=3`
3) `9a+3b+2=-6`

Equations 2 and 3 form a set from which we can calculate that:
`a=8/9` and `b=-5 1/3`