Algebra II.1.B.17 - Modeling with Polynomials—An Introduction – Exit Ticket

Last updated about 4 years ago

5 questions

Jeannie wishes to construct a cylinder closed at both ends. The figure at right
shows the graph of a cubic polynomial function, V, used to model the volume of
the cylinder as a function of the radius if the cylinder is constructed using
150

From EngageNY.org of the New York State Education Department. Grade Algebra II Mathematics Module 1, Topic B, Lesson 17. Internet. Available from https://www.engageny.org/resource/algebra-ii-modul...; accessed 21/Apr/2016.

Algebra II.1.B.17 - Modeling with Polynomials—An Introduction – Exit Ticket

Last updated about 4 years ago

5 questions

Jeannie wishes to construct a cylinder closed at both ends. The figure at right
shows the graph of a cubic polynomial function, V, used to model the volume of
the cylinder as a function of the radius if the cylinder is constructed using
150

Algebra II.1.B.17 - Modeling with Polynomials—An Introduction – Exit Ticket

Algebra II.1.B.17 - Modeling with Polynomials—An Introduction – Exit Ticket

What are the zeros of the function V?

What is the relative maximum value of V, and where does it occur?

The equation of this function is V(r) = c(r3 − 72.25r) for some real number c. Find the value of c so that this formula fits the graph.

Use the graph to estimate the volume of the cylinder with r = 2 cm.

Use your formula for V to find the volume of the cylinder when r = 2 cm. How close is the value from the formula to the value on the graph?

What are the zeros of the function V?

What is the relative maximum value of V, and where does it occur?

The equation of this function is V(r) = c(r3 − 72.25r) for some real number c. Find the value of c so that this formula fits the graph.

Use the graph to estimate the volume of the cylinder with r = 2 cm.

Use your formula for V to find the volume of the cylinder when r = 2 cm. How close is the value from the formula to the value on the graph?