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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 :

naǫ
a.
The equation of the axis of symmetry of a parabola [tex]y=ax^2+bx+c[/tex] is [tex]x=-\frac{b}{2a}[/tex].

[tex]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[/tex]

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

b.
[tex]x=3 \\ \\ h(x)=-x^2+6x \\ h(3)=-3^2+6 \times 3 \\ h(3)=-9+18 \\ h(3)=9[/tex]

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

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