1. What rule would be used to simplify the following? Explain how you would apply this rule for each:
a. 3x0
b. (3x)0
c. -3x0
d. (-3x)0.
2. When you dive from a board that is 32 feet high, the mathematical model -16t2 + 16t + 32 describes your height above the water after t seconds.
a. Factor the polynomial completely.
b. Evaluate both the original polynomial and its factored form for t = 2. Do you get the same answer for each evaluation? Describe what this answer means.
3. An explosion causes debris to rise vertically with an initial speed of 72 feet per second. The formula h = -16t2+ 72t describes the height of the debris above the ground, h, in feet, t seconds after the explosion. How long will it take for the debris to hit the ground? When will the debris be 32 feet above the ground?
4. The radicand of the quadratic formula, b2 - 4ac, can be used to determine whether ax2 + bx + c = 0 has solutions that are rational, irrational, or not real numbers. Explain how this works. Is it possible to determine the kinds of answers that one will obtain for a quadratic equation without actually solving the equation? Explain and provide examples.
Please provide steps and detailed explanations.