How do you write the equation of the parabola in vertex form given Vertex: ( -1, 2), Focus (-1, 0)?

Jul 19, 2017

The vertex form of a parabola where the vertex and the focus are separated by a vertical distance is:

$y = \frac{1}{4 f} {\left(x - h\right)}^{2} + k \text{ [1]}$

Where $\left(h , k\right)$ is the vertex and $f$ is the signed distance from the vertex to the focus.

Substitute the given vertex, $\left(- 1 , 2\right)$, into equation [1]:

$y = \frac{1}{4 f} {\left(x - \left(- 1\right)\right)}^{2} + 2 \text{ [2]}$

Compute the value of $f$ by subtracting the y coordinate of the vertex from the y coordinate of the focus:

$f = 0 - 2$

$f = - 2$

Substitute the value for $f$ into equation [2]:

$y = \frac{1}{4 \left(- 2\right)} {\left(x - \left(- 1\right)\right)}^{2} + 2$

$y = - \frac{1}{8} {\left(x - \left(- 1\right)\right)}^{2} + 2 \text{ [3]}$