# Algebra 2 – Unit 4 – Polynomial and Quadratic Functions

## Standards

 Standard Language A.APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. A.REI.4 Solve quadratic equations in one variables. A.REI.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. A.SSE.3a Factor a quadratic expression to reveal the zero(s) of the function it defines. A.SSE.3b Complete the square in a quadratic to reveal the maximum or minimum value of the function it defines. A.APR.3 Identify zeros of polynomials when suitable factorization are available, and use the zeros to construct a rough graph of the function defined by the polynomials. N.CN.1 Know there is a complex number i such that i2 = -1, and every complex number has the form a + bi with a and b real. N.CN.7 Solve quadratic equations with real coefficients that have complex solutions. F.BF.1 Write a function that describes a relationship between two quantities. F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x+k) for specific values of k (both positive and negative); find the value of k given the graphs.  Experiment with cases and illustrate an explanation of the effects on the graph using technology.

## The “Story” of This Unit

We all know the area of a rectangle is length x width, that’s easy when you know both of those things, but what if they are unknown right now? How do you multiply an unknown by an unknown? This process is very similar to computing area, but very generic. We will explore the “generalized” ways to add, subtract, multiply and divide numbers in general (aka variables). Considering the general leads to some strange conclusions, some that may not exist…seriously, we are going to learn about “imaginary” numbers which is a strange outcome of generalizing with numbers (this also has applications, but we’ll leave that to your pre-calculus teacher). Using functions, graphs, models, and pictures, we will learn about quadratic and polynomial functions.

## Resources

This PhET resource is super helpful for checking answers as you work!