# How do you write the standard form of the equation of the parabola that has a vertex at (8,-7) and passes through the point (3,6)?

##### 1 Answer
Jun 13, 2016

$y = \frac{13}{25} \cdot {\left(x - 8\right)}^{2} - 7$

#### Explanation:

The standard form of a parabola is defined as:

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

where $\left(h , k\right)$ is the vertex

Substitute the value of the vertex so we have:

$y = a \cdot {\left(x - 8\right)}^{2} - 7$

Given that the parabola passes through point $\left(3 , 6\right)$ ,so the coordinates of this point verifies the equation, let's substitute these coordinates by $x = 3$ and $y = 6$

$6 = a \cdot {\left(3 - 8\right)}^{2} - 7$
$6 = a \cdot {\left(- 5\right)}^{2} - 7$
$6 = 25 \cdot a - 7$
$6 + 7 = 25 \cdot a$
$13 = 25 \cdot a$
$\frac{13}{25} = a$

Having the value of $a = \frac{13}{25}$ and vertex$\left(8 , - 7\right)$

The standard form is:

$y = \frac{13}{25} \cdot {\left(x - 8\right)}^{2} - 7$