Question

Each of the "golden arches" at a McDonald's restaurant is in the shape of a parabola. Each arch is modeled by: h(x)= -x^2+6x, where h(x) is the height of the arch (in feet) at a distance x(in feet) from one side.
a. Find the equation of the axis of symmetry.
b. How high is the arch at the axis of symmetry?

Answer 1

A.
The equation of the axis of symmetry of a parabola $y=ax^2+bx+c$ is $x=-\frac{b}{2a}$.

$h(x)=-x^2+6x \\ a=-1 \\ b=6 \\ \\ \hbox{the axis of symmetry:} \\ x=-\frac{6}{2 \times (-1)} \\ x=-\frac{6}{-2} \\ x=-(-3) \\ x=3$

The equation of the axis of symmetry is x=3.

b.
$x=3 \\ \\ h(x)=-x^2+6x \\ h(3)=-3^2+6 \times 3 \\ h(3)=-9+18 \\ h(3)=9$

At the axis of symmetry the arch is 9 feet high.