On the massive, airless planet Krypton, an object falls 50 m in two seconds

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.

4. .

5. .

6. .

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?

Using the information in #8, and again ignoring air resistance, what was the original height of the

9. 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.)