Question

How do you graph `y=1/2(x-3)^2+5`?

Answer 1

Determine the axis of symmetry and the vertex. Determine points on both sides of the axis of symmetry. Sketch a parabola through the points. Do not connect the dots.

Explanation:

`y=1/2(x-3)^2+5` is in vertex form, `y=a(x-h)^2+k`, where `a=1/2, h=3, and k=5`.

The vertex is `(h,k)`, which is `(3,5)`. The axis of symmetry is `x=h=3`

Substitute several values for `x` on both sides of the axis of symmetry to find points on the parabola.

`x=6,` `y=19/2`

`x=5,` `y=7`

`x=4,` `y=11/2`

`x=3,` `y=5` (vertex)

`x=2,` `y=11/2`

`x=1,` `y=7`

`x=0,` `y=19/2`

Plot the points and sketch a curved parabola. Do not connect the dots.

graph{y=1/2(x-3)^2+5 [-16.49, 15.53, 0, 16.01]}