Question

How do you find the axis of symmetry and vertex point of the function: `y = -x^2 - 8x + 10`?

Answer 1

The axis of symmetry is `x=-4`.
The vertex is `(-4,26)`.

Explanation:

`y=-x-8x+10` is a quadratic equation in the form `y=ax+bx+c`, where `a=-1, b=-8, c=10`

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

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

`x=(-b)/(2a)=(-(-8))/(2(-1))=8/(-2)=-4`

The axis of symmetry is `x=-4`.

This is also the `x` value of the vertex.

Vertex
The vertex is the maximum or minimum point of the parabola. Since `a` is a negative number in this equation, the parabola opens downward so the vertex is the maximum point.

Since we know that `x=-4`, we substitute it into the equation and solve for `y`.

`y=-x^2-8x+10`

`y=-(4)^2-(8)(-4)+10=`

`y=-16+32+10=26`

The vertex is `(-4,26)`

graph{y=-x^2-8x+10 [-18.16, 13.86, 14.09, 30.11]}