Question

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

Answer 1

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(-3)=(-3)^2+0.5=9+0.5=9.5`
`y(-2)=(-2)^2+0.5=4+0.5=4.5`
`y(-1)=(-1)^2+0.5=1+0.5=1.5`
`y(0)=(0)^2+0.5=0+0.5=0.5`
`y(1)=(1)^2+0.5=1+0.5=1.5`
`y(2)=(2)^2+0.5=4+0.5=4.5`
`y(3)=(3)^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.