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

Apr 21, 2015

The function is $y = \frac{8}{9} {x}^{2} - \frac{16}{3} x + 2$

Any quadratic function can be written as $y = a {x}^{2} + b x + c$ We know. that the function passes through point $\left(0 , 2\right)$ so $c = 2$.

The vertex of a parabola can be calculated using formula
$V = \left(p , q\right)$ where $p = \frac{- b}{2 a}$.

Third equation comes from the fact that the value of function $f \left(3\right) = - 6$

So we know, that

1) $c = 2$
2) $\frac{- b}{2 a} = 3$
3) $9 a + 3 b + 2 = - 6$

Equations 2 and 3 form a set from which we can calculate that:
$a = \frac{8}{9}$ and $b = - 5 \frac{1}{3}$