Question

How do you find the axis of symmetry, graph and find the maximum or minimum value of the function `y= -(x-5)^2`?

Answer 1

The axis of symmetry is the `x`-value of the minimum or maximum. The max of this function would be `(5,0)`.

Explanation:

To find the axis of symmetry, you must first find the vertex (min or max). If this equation is in vertex form, then you can find your answer without any math, really. It's the `(h,k)` of the vertex form equation.

Vertex form equation:

`y=a(x-h)^2+k`

So, your `(h,k)` of

`y= -(x-5)^2`

would be `(5,0)`.

It's `5` and not `-5` because in the equation there is a `-h`, so you must take the opposite of whatever `h` value is there.

Finally, to find the axis of symmetry, just look at the `x`-value of `(5,0)`:

Axis of Symmetry: `x = 5`

If you look at the graph, the maximum is indeed `(5,0)` and the axis of symmetry is `x = 5`.

graph{-(x-5)^2 [-10, 10, -5, 5]}