# What is the equation of the parabola that has a vertex at  (56, -2)  and passes through point  (53,-9) ?

Dec 27, 2015

$y = - \frac{7}{9} {\left(x - 56\right)}^{2} - 2$

#### Explanation:

The general form of the equation is

$y = a {\left(x - h\right)}^{2} + k$

Given $\textcolor{b l u e}{h = 56} , \textcolor{g r e e n}{k = - 2}$

$\textcolor{red}{x = 53} , \textcolor{p u r p \le}{y = - 9}$

Substitute into the general form of the parabola

color(purle)(-9) = a((color(red)(53)-color(blue)(56))^2 color(green)(-2)
$- 9 = a {\left(- 3\right)}^{2} - 2$

$- 9 = 9 a - 2$

Solve for $a$

$- 9 + 2 = 9 a$

$- 7 = 9 a$

$- \frac{7}{9} = a$

The equation for parabola with the given condition will be

graph{y= -7/9 (x-56)^2 -2 [-10, 10, -5, 5]}