Find the area of the largest rectangle with one corner at the origin, the opposite corner in the first quadrant on the graph of the parabola f(x)=972-4x^2, and sides parallel to the axes. The maximum possible area is

Create a table of values that describes the quadratic function f(x) = 2x ^ 2 - 3x + 5

Determine the vertex of the parabola defined by the quadratic equation y = x^2 - 4x + 3.

Mr. Sample wants you to draw a picture on a piece of paper with 2 inch margins and 1 inch margins on the right and left. He also tells you your drawing must have an area of 20in^2.minimize the length and width of the piece of paper. Using optimization techniques, solve for the length and width.

Determine the maximum area of a rectangle with one side on the -axis and the opposite corners touching the parabola y = x ^ 2 + 9

The Apollo's Chariot is a rollercoaster at Busch Gardens with a top speed of 117 km/hr. Its initial (and tallest) descent can be modeled by h(t) = 52 - 4.9t^2, where h is in meters and t is in seconds. How long does it take to reach the bottom of the hill?    Create a quadratic equation with solutions x=+ square root of five and x=- square root of 5