1. Projectile Motion Students will be able to match up projectile motion graphs with the correct verbal description.

2. FHS Functions 2 Projectile motion is the name given to the path of distance over time that is formed whenever an object is thrown into the air and falls to the ground. This is the same shape that is formed when we graph a quadratic equation. It is called a parabola. It can be expressed as a quadratic equation. Projectile Motion

3. FHS Functions 3 Examples In the assignment you will be asked to match a verbal description to a graph. Here are two verbal descriptions and two graphs. 1.A person stands on a roof and throws a ball up in the air and let it fall to the ground. 2.A person stands on the ground and throws a ball up into the air. The ball lands on a roof. Graph A Graph B Time Height

4. FHS Functions 4 Graphs Now that we have talked about several different functions and the shape of their graphs, let’s see if we can name the type of function based on its graph. Is the graph a linear, exponential, quadratic function, or absolute value? Quadratic Function Absolute Value Function Exponential Function Linear Function

5. FHS Functions 5 Using Tables We can also use a table to determine the type of functions it represents. Remember from the last section - when given a data set, we can determine whether it is a linear or nonlinear function. We look at the rate of change. As long as the change in the x is 1, the rate of change is equal to the change in the y – sometimes called the first difference. If the first difference is constant, then the function is linear.

6. FHS Functions 6 Examples x01234 y-214710 +3 +3 +3 +3 In this table, the first difference (or the rate of change) is constant. That is +3. Therefore, this appears to be a linear function. +1 +1 +1 +1

7. FHS Functions 7 Using Tables When the first difference is not constant, we have to look at the second difference. The second difference is found by subtracting all the first differences from each other. If the second difference is constant, then we have a quadratic function. If the second differences are not constant but follow the same pattern as the first differences, then that indicates an exponential function.

8. FHS Functions 8 Examples x01234 y3461018 x01234 y-4-30512 +1 +3 +5 +7 +1 +2 + 4 +8 In this table, the second difference is the same each time – +2. Therefore, this appears to be a quadratic function. In this table, the second difference is never the same but follows the same pattern as the first difference. Therefore, this appears to be an exponential function. +2 +2 +2 +1 +2 +4

9. FHS Functions 9 Lesson Quiz Let’s see if we can determine what type of function is represented by these tables: Here are some examples: x-2012 y41014 x-2012 y-6-22610 x01234 y024816 Linear Function Quadratic Function Exponential Function