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Question 1

A Minion thrown in to the air starting at zero seconds from an upper floor of a tall building, has a height in feet above the ground t-seconds later given by \(h\left(t\right)=-16t^2+32t+128\) where \(h(t)\) is the height of the ball. When does the ball hit the ground?

Answer: \(t=4\)

Question 2

A company finds out that if it charges \(p\)-dollars for a certain product, it’ll sell \(1800-4p\) of them each year.

  1. At what price will the company price themselves out of the market? That is, have no sales at all?

  2. How much should the company charge to maximize their annual revenue?

Answer: $450 and (225, 202,500)

Question 3

For the function \(f\left(x\right)=x^2+5x+4\), find the following:

  1. The X-intercepts as an ordered pair

  2. The Y-intercepts as an ordered pair

Answer: \((-4,0), (-1,0)\) and \((0,4)\)

Question 4

Solve the following equations

  1. \(3(x-2)^2=27\)

Answer: \(x=5, -1\)

  1. \(x^2-2x=15\)

Answer: \(x=-3,5\)

Question 5

Factor the following equations then solve:

a. \(x^2+8x=-15\)

Answer: \(x=-5,-3\)

b. \(2x^2-5x-3=0\)

Answer: \(x=-\frac{1}{2},3\)

c. \(5m^2+3m=2\)

Answer: \(x=-1,\frac{2}{5}\)

d. \(f(x)=x^2-x-2\)

Answer: \(x=-1,2\)

e. \(x^2+6x+8=0\)

Answer: \(x=-4,-2\)

f. \(x^4+3=4x^2\)

Answer: \(x= \pm 1, \pm \sqrt{3}\)

g. \((2x-3)^2-5(2x-3)+6=0\)

Answer: \(x=\frac{5}{2}, 3\)