# How do you find the equation for the parabola with the vertex (1,4) that passes through the point (3,8)?

##### 1 Answer
Jun 12, 2018

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

#### Explanation:

Given -

Vertex $\left(1 , 4\right)$
Point $\left(3 , 8\right)$

The formula is

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

Where -

$h = 1$
$k = 4$

Then-

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

Find the value of $a$ when one of the points is $\left(3 , 8\right)$

$8 = a {\left(3 - 1\right)}^{2} + 4$
$8 = 4 a + 4$
$4 a + 4 = 8$
$4 a = 8 - 4 = 4$
$4 a = 4$
$a = \frac{4}{4} = 1$
$a = 1$

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

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