Word problem

[Crookshanks]

Suppose you wanted to design a parabolic arch (a parabola opening downward) as a trellis in your garden. This would mean that the first term of the quadratic equation, the term with the variable raised to the second power, would have to be negative. An engineering friend suggests that the following quadratic function might be aesthetically pleasing.

h(x) = -5x2/64 + 4

This function gives the height of the arch (in feet) at any horizontal distance x (in feet) from the centerline of the arch. The trellis (parabola) could be supported by vertical posts at intervals across the inside of the arch. These posts could be placed at 1, 2, 3, 4, 5, 6, and 7 feet on both sides of the centerline (the axis of the parabola). Therefore, for any distance (x-value) the height of a post supporting the arch at that point could be determined from the above function.

Where would the arch touch the ground? (i.e. How far from the axis of the parabola?)

As far as I can get is:
f(x) = (-5 / 64)x^2 + 4
0 = (-5 / 64)x^2 + 4

but I don't know where to go from here. Any suggestions would be appreciated. Thanks.

 

[Guest]

Looks like you now have a quadratic function to solve. This will give you the 2 x points where y=0(ie the ground contact points)

 

[Crookshanks]

no habla algebra. I don't understand what you said there. Could you elaborate for me? Thanks.

for the quadratic function:
h(x) = -5x^2/64 + 4

how would I find out where the arch touches the ground?

would I just solve by setting h(x) to 0? When I do that, I am not sure where to go from there. Thanks for any help