# How do you sketch the graph of y=x^2+0.5 and describe the transformation?

Apr 27, 2017

Pick some easy points for $x$.

#### Explanation:

Let's choose $x = - 3 , - 2 , - 1 , 0 , 1 , 2 , 3$
With these points we get the following
$y \left(- 3\right) = {\left(- 3\right)}^{2} + 0.5 = 9 + 0.5 = 9.5$
$y \left(- 2\right) = {\left(- 2\right)}^{2} + 0.5 = 4 + 0.5 = 4.5$
$y \left(- 1\right) = {\left(- 1\right)}^{2} + 0.5 = 1 + 0.5 = 1.5$
$y \left(0\right) = {\left(0\right)}^{2} + 0.5 = 0 + 0.5 = 0.5$
$y \left(1\right) = {\left(1\right)}^{2} + 0.5 = 1 + 0.5 = 1.5$
$y \left(2\right) = {\left(2\right)}^{2} + 0.5 = 4 + 0.5 = 4.5$
$y \left(3\right) = {\left(3\right)}^{2} + 0.5 = 9 + 0.5 = 9.5$

We can plot the following points to get
graph{x^2+0.5 [-11.21, 11.29, -0.75, 10.5]}
Since 0.5 is added after $x$ is "modified," it will move the function $y = {x}^{2}$ up by half a unit.