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Organizers are launching fireworks over the top of the Washington Monument. Due to costs they would like to find the smallest shell possible that will reach the correct height.

The monument is 555 ft tall. The initial velocities of each size shell are given below.

size – 2 inches

initial velocity ft/s – 117.5

size – 3 inches

initial velocity ft/s – 144

size – 4 inches

initial velocity ft/s – 166

size – 5

initial velocity ft/s – 186

size – 6

initial velocity ft/s – 203.6

The height of the firework t seconds after it is launched is given by

h = -16t^2 + vt where v is the initial velocity.

use the discriminant to determine the smallest size shell that will reach over 555 feet. Explain.

What is the equation for the discriminant for this problem?