Polynomials

Lesson 13

Objective

Identify the solution(s) to systems of polynomial functions.

Common Core Standards

Core Standards

?

  • A.REI.D.11 — Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.

Foundational Standards

?

  • A.REI.D.10

Criteria for Success

?

  1. Explain that the solution to a system of polynomial functions represents the intersection of the two functions. 
  2. Describe that when two functions are set equal to one another you can solve them as a system of equations, and this solution can be seen graphically and proven algebraically. 
  3. Identify the procedures necessary to solve a system of equations, including factoring or use of quadratic formula. 
  4. Describe that, in basic terms, you need the same number of equations as variables.

Anchor Problems

?

Problem 1

What are the intersections of the functions $${f(x)=x^2}$$ and $${g(x)=x^4}$$?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

Illustrative Mathematics Graphs of Power Functions

Graphs of Power Functions, accessed on Sept. 25, 2017, 2:44 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem 2

Below is a graph of the function $${h(x)=3x^3-5x+4}$$ and a graph of the function $${j(x)=-2x+4}$$. For what values does $${h(x)=j(x)}$$? Explain your reasoning algebraically and graphically.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem Set

?

The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

Target Task

?

Using your graphing calculator, find the values of $$x$$ for which $$h(x)=m(x)$$.

$$h(x)=2x^3+2x^2-x+3$$

$$m(x)=(x-4)^2-3$$