Parabola ProblemsDate: 02/23/97 at 19:00:06 From: Cindy Smith Subject: Re: Parabola Problems A culvert is shaped like a parabola, 18 centimeters across the top and 12 centimeters deep. How wide is the culvert 8 centimeters from the top? I have tried setting it up as a complete the square expression, but I haven't been able to get the correct answer of 6sqrt(3). Cindy Smith Date: 03/08/97 at 02:23:22 From: Doctor Luis Subject: Re: Parabola Problems Cindy, Here's a modest diagram of a parabola: ^ y | (-9,12)* | * (9,12) [ 18 cm across the top ] | * | * | * | * | * | * | * | * ---------------*----------------------> x | | The equation for the parabola, in this case, is: y-k = a*(x-h)^2 y = a * x^2 Since you know that the point (9,12) is on the parabola: 12 = a * 9^2 12 = 81a a = 12/81 = 4/27 Now the equation is: y = (4/27)*x^2 If you're 8 cm from the TOP (I'm considering the top to be y = 12), then you're at (x,12-8) = (x,4) [we still haven't found x for this point]. Therefore: 4 = (4/27) * x^2 x^2 = 4*27/4 = 27 x = sqrt(27) = 3 * sqrt(3) Since x represents the half-width of the parabola, the width at 8 cm from the top is: 2x = 6 * sqrt(3) -Doctor Luis, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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