# How do you graph y=(x-3)^2 +5?

Dec 7, 2017

The graph should look like this: graph{(x-3)^2+5 [-10, 10, -5, 5]}

#### Explanation:

First, since the equation is in the vertex form $a {\left(x - h\right)}^{2} + k$, we find the a, h, and k.

In the function $y = {\left(x - 3\right)}^{2} + 5$, $a = 1$, $h = 3$, and $k = 5$

Now, we plot the points.

We plot the points by using the following diagram:
Remember that when you plug in h, you always get k.
x======y
$h - 2 a$
$h - a$
$h$ => $k$
$h + a$
$h + 2 a$

Plug these values in the function to get the y coordinates.

x======y
$3 - 2 \left(1\right)$
$3 - 1$
$3$
$3 + 1$
$3 + 2 \left(1\right)$

x==y
$1$=>$9$
$2$=>$6$
$3$=>$5$
$4$=>$6$
$5$=>$9$

Plot these points and you have the answer!