# What is the equation of the parabola that has a vertex at  (-18, 2)  and passes through point  (-3,-7) ?

##### 1 Answer
Apr 26, 2017

In vertex form we have:

$y = - \frac{1}{25} {\left(x + 18\right)}^{2} + 2$

#### Explanation:

We can use the vertex standardised form:

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

As the vertex $\to \left(x , y\right) = \left(\textcolor{g r e e n}{- 18} , \textcolor{red}{2}\right)$

Then $\left(- 1\right) \times d = \textcolor{g r e e n}{- 18} \text{ "=>" } d = + 18$

Also $k = \textcolor{red}{2}$
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So now we have:

$y = a {\left(x + d\right)}^{2} + k \text{ "->" } y = a {\left(x + 18\right)}^{2} + 2$

Using the given point of $\left(- 3 , - 7\right)$ we substitute to determine $a$

$y = a {\left(x + 18\right)}^{2} + 2 \text{ "->" } - 7 = a {\left(- 3 + 18\right)}^{2} + 2$

$\text{ } - 7 = 225 a + 2$

$\text{ } \frac{- 7 - 2}{225} = a$

$\text{ } a = - \frac{1}{25}$

Thus $y = a {\left(x + d\right)}^{2} + k \text{ "->" } y = - \frac{1}{25} {\left(x + 18\right)}^{2} + 2$