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

Aug 21, 2015

Determine the vertex. Plot the vertex and several points. Draw the parabola as an upward facing curve.

#### Explanation:

$y = {\left(x - 3\right)}^{2} + 5$ is in the vertex form of a parabola, $y = {\left(x - h\right)}^{2} + k$, where $h = 3$ and $k = 5$. The vertex of this parabola is $\left(h , k\right) = \left(3 , 5\right)$.

Find some points by substituting values for $x$, making sure to include both positive and negative values.

$x = - 2 ,$ $y = 30$
$x = - 1 ,$ $y = 21$
$x = 0 ,$ $y = 14$
$x = 1 ,$ $y = 9$
$x = 2 ,$ $y = 6$

Plot the vertex, and then some points. Draw a graph as a curve where the curve turns at the vertex $\left(3 , 5\right)$.

graph{y=(x-3)^2+5 [-16.82, 15.2, 2.24, 18.25]}