# How do you write the standard Form of the parabola equation given Vertex (3 , -3) Focus (3 , -9/4)?

May 24, 2017

$y = \frac{1}{3} \left({x}^{2} - 6 x\right)$

#### Explanation:

Look at the diagram

Given -
Vertex $\left(3 , - 3\right)$
Focus 3, -9/4)

The parabola is facing up. Hence the equation-

${\left(x - h\right)}^{2} = 4 a \left(y - k\right)$

Where -

$h = 3$
$k = - 3$
$a = \frac{3}{4}$ [Distance between vertx and focus]

${\left(x - 3\right)}^{2} = 4 \times \frac{3}{4} \times \left(y - \left(- 3\right)\right)$
x^2-6x+9)=3(y+3)=3y+9

$3 y + 9 = {x}^{2} - 6 x + 9$
$3 y = {x}^{2} - 6 x \cancel{+ 9} \cancel{- 9}$
$y = \frac{1}{3} \left({x}^{2} - 6 x\right)$