# How do you write the vertex form of a parabola with (3,2.5) and (4,5.5)?

Jul 18, 2018

$y = 3 {\left(x - 3\right)}^{2} + 2.5$

#### Explanation:

Let us take $\left(3 , 2.5\right)$ the vertex and passes through the point $\left(4 , 5.5\right)$

The vertex form of the equation formula is -

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

Where -

$h = 3$
$k = 2.5$

Then -

$y = a {\left(x - 3\right)}^{2} + 2.5$

To find the value of $k$, assume the parabola is passing through the point $\left(4 , 5.5\right)$

Then -

$a {\left(4 - 3\right)}^{2} + 2.5 = 5.5$

$a + 2.5 = 5.5$

$a = 5.5 - 2.5 = 3$

Plug in the value $a = 3$ in $y = a {\left(x - 3\right)}^{2} + 2.5$

$y = 3 {\left(x - 3\right)}^{2} + 2.5$