Help Please

Question

A ball is thrown straight up, from 11 meters above the ground, with a velocity of 7 m/s. The equation below models the height of the ball:
h = -4t^(2) + 7t +11

a. Use the discriminant to determine the number and type of solutions for the quadratic equation.
b. Graph the equation to verify the result that the discriminant indicated.
c. Solve the equation by graphing, factoring, and the quadratic formula.
d. What do you notice about each method?
e. Describe what the solutions mean in context of the problem.
f. Describe the domain of this problem.

Answer 1

discriminate = b^2 - 4ac = 49+4(4)(11) > 0 so there are 2 solutions

graphically the solutions are the x intercepts, where the parabola intersects the x axis

x= 7/8 + or - (1/8)sqr(225) = 7/8 + 15/8= 22/8 = 2.75 second when it comes down and hits the ground level

(-4x+11)(x+1) = 0

x=-1, x= 11/4 = 2.75 seconds,

ignore the negative solution

-4t^2 + 7t = -11

t^2 - 7t/4 + 49/64 = 11/4 + 49/64 = 225/64

t-7/8 = 15/8

t = 15/8 + 7/8 = 2.75 seconds

the 3 methods give the same result, 2.75 seconds to hit ground

domain is [0,2.75]