SOLUTION: A parabolic arch has a height of 20 m and a width of 36 m at the base. If the vertex of the parabola is at the top of the arch, at which height above the base is it 18 m wide?

Question 768162: A parabolic arch has a height of 20 m and a width of 36 m at the base. If the vertex of the parabola is at the top of the arch, at which height above the base is it 18 m wide?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
A parabolic arch has a height of 20 m and a width of 36 m at the base. If the vertex of the parabola is at the top of the arch, at which height above the base is it 18 m wide?
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Representing the arch, draw a parabola that opens downward with the the vertex at (0,20).
Standard form of equation: y=A(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex
y=A(x-0)^2+20
y=Ax^2+20
Using coordinates of right side of the base(18,0)to find A
0=A(18^2)+20
-20=324A
A=-20/324=-5/81
When arch is 18m wide, x=9
y=(-5/81)(9^2)+20=15m
height above the base when arch is 18 m wide=15m
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