Modeling With Quadratic Functions Section 2.4 beginning on page 76.

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Modeling With Quadratic Functions Section 2.4 beginning on page 76

By the End of This Section… You will know how to choose the appropriate form of a quadratic equation to use depending on the information given. **We will come back to this as we are learning how to solve three variable linear systems. ***

Example 1: The graph shows the parabolic path of a performer who is shot out of a cannon, where y is the height (in feet) and x is the horizontal distance traveled (in feet). Write an equation of the parabola. The performer lands in a net 90 feet from the cannon. What is the height of the net? Given: Vertex:Point: Substitute the values from the vertex and the point into vertex form to find the value of a. Now find the height when x = 90 (where the performer lands) The height of the net is 22 feet. Use the values of a, h, and k to write the equation

2) Write an equation of the parabola that passes through the point (-1,2) and has a vertex of (4,-9) Given: Vertex:Point: Substitute the values from the vertex and the point into vertex form.

a) Write a function f that models the temperature over time. What is the coldest temperature? The lowest temp is the minimum. b) What is the average rate of change in temperature over the interval in which the temperature is decreasing? Increasing? Compare the average rates of change. -10c is the lowest temp. Example 2: A meteorologist creates a parabola to predict the temperature tomorrow, where x is the number of hours after midnight and y is the temperature (in degrees Celsius).

Given a Point and the x-intercepts 4) Write an equation of the parabola that passes through the point (2,5) and has x-intercepts -2 and 4.

The optimal driving speed is about 49 mph.

Practice Quadratic Regression