# What is the equation of the parabola that has a vertex at  (-8, 5)  and passes through point  (2,27) ?

${\left(x - - 8\right)}^{2} = + \left(\frac{50}{11}\right) \left(y - 5\right) \text{ }$Vertex Form

#### Explanation:

From the given: Vertex (-8, 5) and passing thru (2, 27), the parabola opens upward. The reason is that the vertex is lower than the given point.

By the vertex form , we can solve for the value of $p$

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

${\left(2 - - 8\right)}^{2} = + 4 p \left(27 - 5\right)$

${10}^{2} = 4 p \left(22\right)$

$100 = 4 \left(22\right) p$

$25 = 22 p$

$p = \frac{25}{22}$

Go back to the vertex form

${\left(x - - 8\right)}^{2} = + 4 \left(\frac{25}{22}\right) \left(y - 5\right)$

${\left(x - - 8\right)}^{2} = + 2 \left(\frac{25}{11}\right) \left(y - 5\right)$

${\left(x - - 8\right)}^{2} = + \left(\frac{50}{11}\right) \left(y - 5\right) \text{ }$Vertex Form

graph{(x--8)^2=(50/11)(y-5)[-50,50,-25,25]}

God bless....I hope the explanation is useful.