Question

How do you graph `y= (x-4)^2 +3`?

Answer 1

Determine the vertex and several points, preferably on mirror images of the parabola. Plot points and sketch a curve through the points. Do not connect the dots.

Explanation:

`y=(x-4)^2+3`

The equation is in vertex form, `y=a(x-h)^2=k`, where `(h,k)` is the vertex, and `a=1`, `h=4`, and `k=3`. The vertex `(h,k)=(4,3)`.

Determine several points on the parabola, substituting both positive and negative numbers for `x`, and making sure to get points on both sides of the parabola. A mirror image is preferred. `y=(x-4)^2+3`

`x=0,` `y=19`
`x=1,` `y=12`
`x=2,` `y=7`
`x=6,` `y=7`
`x=7,` `y=12`
`x=8,` `y=19`

Plot the vertex and the points that you determined. Sketch a parabola (curve) through the points with the vertex as the minimum point. Do not connect the dots.

graph{y=(x-4)^2+3 [-15.09, 16.93, -1.09, 14.93]}