A graphing device is recommended.

In this problem you are asked to find a function that models a real$-$life situation and then use the model to answer questions about the situation. Use the Guidelines for Modeling with Functions to help you.

Find the dimensions that give the largest area for the rectangle shown in the figure.

The x$$y$-$coordinate plane is given. A curve and a rectangle are given.

The curve labeled y $=7$ x$2$ enters the window in the third quadrant, goes up and right becoming less steep, crosses the negative x$-$axis, changes direction at a point on the positive y$-$axis, goes down and right becoming less steep, passes through the point $($x$,$ y$),$ crosses the positive x$-$axis, and exits the window in the fourth quadrant.

The rectangle has its base on the x$-$axis and is centered on the positive y$-$axis.

The top right corner of the rectangle touches the curve at the point $($x$,$ y$).$

Its base is on the x$-$axis and its other two vertices are above the x$-$axis, lying on the parabola

y $=7$ x$2.$

$($Round your answers to two decimal places.$)$