SOLUTION: I'm having promblems understanding how to find the info i need to graph this equation..... I could possibly have the wrong equation. L x 15 -L ( this is the eqution I came up

Question 133489This question is from textbook frogs, fleas, and painted cubes
: I'm having promblems understanding how to find the info i need to graph this equation.....
I could possibly have the wrong equation.
L x 15 -L ( this is the eqution I came up with)
the original equation is .... The rectangle has a perimeter of 30 meters and a side length of l, A=?
Thank you for your help This question is from textbook frogs, fleas, and painted cubes

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
So far, so good.

is absolutely correct. But you probably want to put this into standard form:

This is just a quadratic in the form , substituting L for the independent variable x and with coefficients as follows:

The vertex of the parabola has an x-coordinate at , so

The y-coordinate of the vertex is equal to the value of the function at the x-coordinate, so

Hence the vertex of the graph is at (15/2,225/4).

Factors of are , so zeroes of the polynomial are 0 and 15, meaning the x-intercepts are at (0,0) and (15,0).

Pick a couple other values for L:

If L = 1, then , and by symmetry, if L = 14, A = 14

If L = 2, then , and by symmetry, if L = 13, A = 26

Just plot the points and sketch a smooth curve.

Super-Double-Plus Extra Credit. Just looking at this picture, what specific quadrilateral gives the maximum area for a given perimeter?
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