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

1 Answer
Meave60
Oct 7, 2015

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]}

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