The perimeter of a rectangle is 540 feet. Let x = the width of rectangle. Write a quadratic function for the area of the rectangle in terms of its width. Find the vertex of the graph of the quadratic function and interpret its meaning in the context of the problem. Please Help!

The perimeter of a rectangle is 540 feet. Let x = the width of rectangle. Write a quadratic function for the area of the rectangle in terms of its width. Find the vertex of the graph of the quadratic function and interpret its meaning in the context of the problem. Please Help!

@Mathematics

Question

The perimeter of a rectangle is 540 feet. Let x = the width of rectangle. Write a quadratic function for the area of the rectangle in terms of its width. Find the vertex of the graph of the quadratic function and interpret its meaning in the context of the problem. Please Help!

@Mathematics

anonymous · Answer

If the width is x, then the length is 270 - x

anonymous · Answer

Area would be   x(270-x)

anonymous · Answer

Area = -x^2 + 270x

anonymous · Answer

okay i had got 270x-x^2

anonymous · Answer

okay so then is it (135, 18225)

anonymous · Answer

This quadratic function would open downward  so you would have a maximum point..  which would have an (x,y) point..  The x representing the width of that rectangle and y representing the area of that rectangle.   so the vertex represents the x value you would need to have the largest area

anonymous · Answer

yes.

anonymous · Answer

so to show my work i would complete the square?