Question

How do you find the axis of symmetry and vertex point of the function: `y= -x^2-4x+5`?

Answer 1

The axis of symmetry is `x=-2`.
The vertex is `(-2,9)`.

Explanation:

`y=-x^2-4x+5` is a quadratic equation in the form `y=ax+bx+c`, where `a=-1, b=-4, and c=5`.

Axis of Symmetry
An imaginary vertical line that divides the parabola into two equal halves. The formula for determining the axis of symmetry is `x=(-b)/(2a)`

`x=(-(-4))/((2*-1))=4/(-2)=-2`

The axis of symmetry is `x=-2`

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

The `x` value for the vertex is the same as the axis of symmetry. To find the `y` value, substitute `-2` for `x` in the equation. Solve for `y`.

`y=-x^2-4x+5`

`y=-(-2)^2-4(-2)+5=`

`y=-4+8+5=9`

The vertex is `(-2,9)`.

graph{y=-x^2-4x+5 [-14.95, 13.52, -3.76, 10.48]}