4.3 – Modeling with Quadratic Functions Three noncollinear points, no two of which are in line vertically, are on the graph of exactly one quadratic function.

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Presentation transcript:

4.3 – Modeling with Quadratic Functions Three noncollinear points, no two of which are in line vertically, are on the graph of exactly one quadratic function.

4.3 – Modeling with Quadratic Functions Problem 1: A parabola contains the points (0,0), (-1, -2), and (1, 6). What is the equation of this parabola in standard form?

4.3 – Modeling with Quadratic Functions Problem 1: A parabola contains the points (0,0), (1, -2), and (-1, -4). What is the equation of this parabola in standard form?

4.3 – Modeling with Quadratic Functions Problem 1: A parabola contains the points (-1,6), (1, 4), and (2, 9). What is the equation of this parabola in standard form?

4.3 – Modeling with Quadratic Functions Problem 2: Determine whether a quadratic model exists for each set of values. If so, write the model. f(-2) = 16; f(0) = 0; f(1) = 4

4.3 – Modeling with Quadratic Functions Problem 2: Determine whether a quadratic model exists for each set of values. If so, write the model. f(-1) = -4; f(1) = -2; f(2) = -1

4.3 – Modeling with Quadratic Functions Problem 2: Campers at an aerospace camp launch rockets on the last day of camp. The path of Rocket 1 is modeled by the equation h = -16t t + 1 where t is the time in seconds and h is the distance from the ground. The path of Rocket 2 is modeled by the graph at the right. Which rocket flew higher? Which rocket stayed in the air longer? What is a reasonable domain and range for each function?

4.3 – Modeling with Quadratic Functions Problem 3: The table shows a meteorologist’s predicted temperatures for an October day in Sacramento, California. What is a quadratic model for this data? Predict the high temp for the day. At what time does this occur?

4.3 – Modeling with Quadratic Functions Problem 3: The table shows a meteorologist’s predicted temperatures for a summer day in Denver, Colorado. What is a quadratic model for this data? Predict the high temp for the day. At what time does this occur?

4.3 – Modeling with Quadratic Functions Problem 3: Find a quadratic model for the data. Use 1981 as year 0. Describe a reasonable domain and range for your model (Hint: This is a discrete, real situation) Estimate when first class postage was 37 cents.