U5 L3: Modeling With Quadratic Functions

1. What is the equation, in standard form, of a parabola that contains the following points (-2, 18), (0, 2), (4, 42)?

2. What is the equation in standard form of a parabola that models the values in the table?

3. A biologist took a count of the number of migrating waterfowl at a particular lake and recounted the lake's population of waterfowl on each of the next six weeks. Find a quadratic function that models the data as a function of x, the number of weeks. Use the model to estimate the number of waterfowl at the lake on week 8.

4. The table shows a meteorologist's predicted temperatures for an April day in Washington D.C. Use quadratic regression to find a quadratic model for this data. (Use the 24-hour clock to represent times after noon.)

5. Suppose the function, g(x), is used to model the height ,y, of a soccer ball, x seconds after the ball is kicked up in the air. The ball starts on the ground and travels in a parabolic shape as it reaches a maximum height and then returns to the ground. Suppose further that the ball reaches its maximum height of 15 feet in 2.2 seconds. What would be an appropriate domain for g(x)?