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 = -16t2 + 150t + 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.