Problems 1-3: Determine the vertex of the parabolas defined by the following functions:
1. F(x) = x2 – 4
2. G(x) = -2x2 + 8x – 15
3. H(x) = .5(x – 3)2 + 5
Problems 4-6: Complete the tables for the following functions, and provide a graph.
Problem 7. For each equation, determine the number and type of solutions by calculating the value of the discriminant.
8. A ball is dropped from a height of 40 meters. The quadratic equation
d = .5gt2
is used to calculate the distance d the object has fallen (ignoring the resistance of the atmosphere) after t seconds, where the constant “g” is the acceleration due to the earth’s gravity, approximately 9.8 m/s2. How long does it take the object to fall to the ground?
9. Using the information in #8, and again ignoring air resistance, what was the original height of the object if it takes 5 seconds for it to reach the ground?
10. On the massive, airless planet Krypton, an object falls 50 m in two seconds. What is the acceleration of gravity -- that is, the local value of g -- on Krypton? (NOTE: Krypton is an imaginary place. Don't bother Googling it.)