Illustrative Math - Algebra 2 - Unit 2 - Lesson 14

By Formative Library

Last updated about 1 year ago

7 Questions

We know these things about a polynomial function, f(x): it has exactly one relative maximum and one relative minimum, it has exactly three zeros, and it has a known factor of (x-4). Sketch a graph of f(x) given this information.

A.APR.2

A.APR.3

Mai graphs a polynomial function, f(x), that has three linear factors (x+6), (x+2), and (x-1). But she makes a mistake. What is her mistake?

A.APR.2

A.APR.3

Here is the graph of a polynomial function with degree 4.
Select all of the statements that are true about the function.

One of the factors is (x-1).

It has 2 relative maximums.

One of the zeros is x=2.

The constant term is negative.

It has 4 linear factors.

There is a relative minimum between x=1 and x=3.

The leading coefficient is positive.

A.APR.2

A.APR.3

State the degree and end behavior of f(x)=2x^{3}-3x^{5}-x^{2}+1. Explain or show your reasoning.

A.APR.2

A.APR.3

Is this the graph of g(x)=(x-1)^{2}(x+2) or h(x)=(x-1)(x+2)^{2}? Explain how you know.

A.APR.2

A.APR.3

Kiran thinks he knows one of the linear factors of P(x)=x^{3}+x^{2}-17x+15. After finding that P(3)=0, Kiran suspects that x-3 is a factor of P(x), so he sets up a diagram to check. Here is the diagram he made to check his reasoning, but he set it up incorrectly. What went wrong?

A.APR.2

A.APR.3

The polynomial function B(x)=x^{3}+8x^{2}+5x-14 has a known factor of (x+2). Rewrite B(x) as a product of linear factors.

A.APR.2

A.APR.3

This lesson is from Illustrative Mathematics. Algebra 2, Unit 2, Lesson 14. Internet. Available from https://curriculum.illustrativemathematics.org/HS/teachers/3/2/14/index.html ; accessed 27/July/2021.

IM Algebra 1, Geometry, Algebra 2 is © 2019 Illustrative Mathematics. Licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.

These materials include public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses. See the image attribution section for more information.