Question 468084: A lab designed radio telescope with diaeter of 320 ft & maximum depth of 42 ft Find the equation of the parabola and graph.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A lab designed radio telescope with diameter of 320 ft & maximum depth of 42 ft Find the equation of the parabola and graph.
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Standard form for a parabola: y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex.
Given radio telescope is a parabola that opens upwards.
Draw a diagram with the left side of the parabola at the origin, (0,0) and the right side at (320,0) Coordinates of the vertex are at (160,-42). This also gives the parabola an axis of symmetry at x=160.
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y=A(x-h)^2+k
using (x,y) coordinates of one point (0,0) on the curve and (x,y) coordinates of the vertex:
0=A(0-160)^2-42
A=42/(-160)^2=42/25600=.0016
Equation of parabola:
y=.0016(x-160)^2-42
See graph below:
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