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=-(b)/(2a)`.


`h(x)=-x^2+6x \\ a=-1 \\ b=6 \\ \\ \hbox{the axis of symmetry:} \\ x=-(6)/(2 * (-1)) \\ x=-(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 * 3 \\ h(3)=-9+18 \\ h(3)=9`

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