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

1 Answer
Meave60
Oct 20, 2015

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]}

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