Question

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

Answer 1

The graph should look like this: graph{(x-3)^2+5 [-10, 10, -5, 5]}

Explanation:

First, since the equation is in the vertex form `a(x-h)^2+k`, we find the a, h, and k.

In the function `y=(x-3)^2+5`, `a=1`, `h=3`, and `k=5`

Now, we plot the points.

We plot the points by using the following diagram:
Remember that when you plug in h, you always get k.
x======y
`h-2a`
`h-a`
`h` => `k`
`h+a`
`h+2a`

Plug these values in the function to get the y coordinates.

x======y
`3-2(1)`
`3-1`
`3`
`3+1`
`3+2(1)`

x==y
`1`=>`9`
`2`=>`6`
`3`=>`5`
`4`=>`6`
`5`=>`9`

Plot these points and you have the answer!