How do you find the axis of symmetry and vertex point of the function: y=−x2−8x+10?

1 Answer
Meave60
Oct 7, 2015

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=−b2a.

x=−b2a=−(−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=−x2−8x+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]}

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