Question

How do you find the axis of symmetry and vertex point of the function: `f(x) = -x^2 + 10`?

Answer 1

The axis of symmetry is `x=0`.
The vertex is `(0,10)`.

Explanation:

`f(x)=-x^2+10`

Substitute `y` for `f(x)`.

`y=-x^2+10` is a quadratic equation in the form `ax^2+bx+c`, where `a=-1, b=0, c=10`.

Axis of symmetry
The axis of symmetry is an imaginary horizontal line that divides the parabola into two equal halves.

The formula for finding the axis of symmetry is `x=(-b)/(2a)`

`x=(-b)/(2a)=(0)/(2*-1)=0`

The axis of symmetry is `x=0`.

Vertex
The vertex is the maximum or minimum point on the parabola. In this case, because `a` is negative, the parabola opens downward and so the vertex is the maximum point.

The `x` value of the vertex is `0`.

To find the `y` value of the vertex is determined by substituting the `x` value into the equation and solving for `y`.

`y=-(0)^2+10=10`

The vertex is `(0,10)`.

graph{y=-x^2+10 [-16.82, 15.2, -4.1, 11.92]}