SOLUTION: A rectangle is placed under the parabolic arch given by f(x)=27-3x^2 by using a point (x,y) on the parabola, as shown in the figure. Write a formula for the function A(x) that give

Question 16794: A rectangle is placed under the parabolic arch given by f(x)=27-3x^2 by using a point (x,y) on the parabola, as shown in the figure. Write a formula for the function A(x) that gives the area of the rectangle as a function of the x-coordinate of the point chosen.

The figure is basically an arc with a square underneath it with the top left and right side of the square touching the arc on either side. There is a line drawn from the center of the top of the arc to the bottom. 0 is at the bottom of the center line and x is at the bottom of the right line of the square. (x,y) is at the top of the right side of the square. f(x) is on the left side of the arc and square.

I know A=LxWxH. I'm not sure how to applies to A(x).

Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
The function A(x) is obviously the area beneath the rectangle formed under the parabolic arch f(x) = 27-3x^2. The rectangle has a width of 2x, and the height of the rectangle is y which equals 27-3x^2. Since Area = width * length,
A(x) = .

This could also be expanded:
A(x) = or it could be factored completely:
A(x) = .

R^2 at SCC

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