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4.3 Modeling with Quadratic Functions P209-211. Ex 1) Write an equation in standard form of the parabola passing through the points (0,0), (-1,-2), (1,6).

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Presentation on theme: "4.3 Modeling with Quadratic Functions P209-211. Ex 1) Write an equation in standard form of the parabola passing through the points (0,0), (-1,-2), (1,6)."— Presentation transcript:

1 4.3 Modeling with Quadratic Functions P209-211

2 Ex 1) Write an equation in standard form of the parabola passing through the points (0,0), (-1,-2), (1,6).

3 Ex) The table shows a meteorologist’s predicted temperatures for an October day in Sacramento, California. Find a quadratic model for this data. TimePredicted Temperature (F) 8AM52 10AM64 12PM72 2PM78 4PM81 6PM76

4 The diagram shows the path of a model rocket launched from the ground. It reaches a maximum altitude of 384 ft when it is above a location 16 ft from the launch site. What quadratic function models the height of the rocket?

5 The amount of cloth used to make four curtains is given by the function, where x is the width of one curtain in feet and A is the total area in square feet. Find the width that maximizes the area of the curtains and then find the maximum area.

6 A small independent motion picture company determines the profit P for producing n DVD copies of a recent release is P =  0.02n 2 + 3.40n  16. P is the profit in thousands of dollars and n is in thousands of units. Determine how many DVDs the company should produce to maximize the profit. Then find the maximum profit.

7 To line an irrigation ditch, a farmer will use rectangular metal sheets. Each side will be bent x feet from the edge at an angle of 90 ° to form the trough. If the sheets are 20 ft wide, how far from the edge (x) should the farmer bend them to maximize the area of a cross-section of the trough.

8 Time, sheight, ft 046 163 248 31 A man throws a ball off the top of a building and records the height of the ball at different times, as shown in the table. Find a quadratic model for the data. Use the model to estimate the height of the ball at 2.5 seconds, the find the ball’s maximum height.


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