Francine7420
Answered

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.

AFind the equation of the axis of symmetry.
BHow high is the arch at the axis of symmetry?

Verified Answer :

naǫ

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.

Related Questions