# How do I graph the quadratic equation y=1/4(x-2)^2+4?

Nov 10, 2014

A way to graph $y = \frac{1}{2} {\left(x - 2\right)}^{2} + 4$ is to find the vertex and then create a table of values to graph. Since the equation is in vertex form ($y = a {\left(x - h\right)}^{2} + k$), we know the vertex (h,k) is $\left(2 , 4\right)$. This helps to focus on which x values to use, since the vertex must be in the middle.

Now to create a table: (choose an x value, plug it into the equation to find a y value)
(x,y)
$x = 0 , y = \frac{1}{2} {\left(0 - 2\right)}^{2} + 4 \implies y = \frac{1}{2} {\left(- 2\right)}^{2} + 4 \implies y = \frac{1}{2} \left(4\right) + 4 \implies y = 2 + 4 \implies y = 6$

$\left(0 , 6\right)$

$x = 1 , y = \frac{1}{2} {\left(1 - 2\right)}^{2} + 4 \implies y = \frac{1}{2} {\left(- 1\right)}^{2} + 4 \implies y = \frac{1}{2} \left(1\right) + 4 \implies y = \frac{1}{2} + 4 \implies y = 4.5 \left(4 \frac{1}{2}\right)$

$\left(1 , 4.5\right)$

Vertex $\left(2 , 4\right)$

(the next values should match x=1 and x=0 since quadratics are symmetric)

$x = 3 , y = \frac{1}{2} {\left(3 - 2\right)}^{2} + 4 \implies y = \frac{1}{2} {\left(1\right)}^{2} + 4 \implies y = \frac{1}{2} \left(1\right) + 4 \implies y = \frac{1}{2} + 4 \implies y = 4.5 \left(4 \frac{1}{2}\right)$

$\left(3 , 4.5\right)$

$x = 4 , y = \frac{1}{2} {\left(4 - 2\right)}^{2} + 4 \implies y = \frac{1}{2} {\left(2\right)}^{2} + 4 \implies y = \frac{1}{2} \left(4\right) + 4 \implies y = 2 + 4 \implies y = 6$

$\left(4 , 6\right)$

Now graph the following points:
$\left(0 , 6\right) , \left(1 , 4.5\right) , \left(2 , 4\right) , \left(3 , 4.5\right) , \left(4 , 6\right)$

Connect the dots, graph should be shaped as "u". That is the graph of the quadratic equation $y = \frac{1}{2} {\left(x - 2\right)}^{2} + 4$.