Question

How do you find the axis of symmetry, graph and find the maximum or minimum value of the function `y-4 = – 2(x – 1)^2`?

Answer 1

The axis of symmetry is `x=1`.
The vertex is `(1,4)`.

Explanation:

`y-4=-2(x-1)^2`

Put the equation into vertex form, `y=a(x-h)^2+k`, by adding `4` to both sides of the equation.

`y=-2(x-1)^2+4`, where `a=-2, h=1, k=4`

The axis of symmetry is the vertical line that divides a parabola into two equal halves. For an equation in vertex form, the axis of symmetry is `x=h`.

The axis of symmetry is `x=1`.

The vertex is the minimum or maximum point of a parabola. In this case, because `a=-2`, the parabola opens downward and the vertex is the maximum point.

The vertex in vertex form is `(h,k)`.
The vertex is `(1,4)`.

graph{y=-2(x-1)^2+4 [-10, 10, -5, 5]}