# How do you write the equation of the parabola in vertex form given (-2,3) and focus (0,3)?

Feb 10, 2018

${\left(y - 3\right)}^{2} = 8 \left(x + 2\right)$

#### Explanation:

Given -

Vertex $\left(- 2 , 3\right)$
Focus $\left(0 , 3\right)$

The vertex is in the 2nd quadrant.
The focus is to the right of the vertex.
The parabola opens right.

The general form of such a parabola is

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

Where -

$k = 3 \to$ y - coordinate of the vertex
$h = - 2 \to$ x - coordinate of the vertex
$a = 2 \to$ Distance between the vertex and the focus

Substitute these values in the given formula

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

${\left(y - 3\right)}^{2} = 8 \left(x + 2\right)$