# How do you graph y=1/2(x-3)^2+5?

Sep 20, 2015

Determine the axis of symmetry and the vertex. Determine points on both sides of the axis of symmetry. Sketch a parabola through the points. Do not connect the dots.

#### Explanation:

$y = \frac{1}{2} {\left(x - 3\right)}^{2} + 5$ is in vertex form, $y = a {\left(x - h\right)}^{2} + k$, where $a = \frac{1}{2} , h = 3 , \mathmr{and} k = 5$.

The vertex is $\left(h , k\right)$, which is $\left(3 , 5\right)$. The axis of symmetry is $x = h = 3$

Substitute several values for $x$ on both sides of the axis of symmetry to find points on the parabola.

$x = 6 ,$ $y = \frac{19}{2}$

$x = 5 ,$ $y = 7$

$x = 4 ,$ $y = \frac{11}{2}$

$x = 3 ,$ $y = 5$ (vertex)

$x = 2 ,$ $y = \frac{11}{2}$

$x = 1 ,$ $y = 7$

$x = 0 ,$ $y = \frac{19}{2}$

Plot the points and sketch a curved parabola. Do not connect the dots.

graph{y=1/2(x-3)^2+5 [-16.49, 15.53, 0, 16.01]}