Question

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

Answer 1

Determine the vertex. Plot the vertex and several points. Draw the parabola as an upward facing curve.

Explanation:

`y=(x-3)^2+5` is in the vertex form of a parabola, `y=(x-h)^2+k`, where `h=3` and `k=5`. The vertex of this parabola is `(h,k)=(3,5)`.

Find some points by substituting values for `x`, making sure to include both positive and negative values.

`x=-2,` `y=30`
`x=-1,` `y=21`
`x=0,` `y=14`
`x=1,` `y=9`
`x=2,` `y=6`

Plot the vertex, and then some points. Draw a graph as a curve where the curve turns at the vertex `(3,5)`.

graph{y=(x-3)^2+5 [-16.82, 15.2, 2.24, 18.25]}