Intro to Polynomials 3-1

Intro to Polynomials 3-1

Intro to Polynomials

​Algebra 2

​Lesson Overview

​Objectives:

​

1. ​ Graph Polynomial function and show the key features of a graph

2. ​ Predict the end behavior of polynomial functions by interpreting the leading coefficients and degrees

3. ​ Sketch graphs showing key features, given a variable description

​

​Visual Interpretations of Odd Exponents

​Visual Interpretation of Even exponents

​Graph:

​y= 2x²

​

y= -2x²

​

​

​What does the leading coefficient tell us about the graph?

Multiple Select

Odd exponents passes through which quadrant? Choose all that apply

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

Multiple Select

Even exponents passes through which quadrant? Choose all that apply

• Quadrant I

• Quadrant II

• QUadrant III

• Quaadrant IV

Multiple Choice

Which function would be in quadrant I and III

• f(x)= $$2x^2$$  

• f(x) =  $$4x^3$$  

• Neither

• Both

Standard form of a Polynomial

​

​Standard form of a Polynomial

​

​Standard form of a polynomial shows ay like terms combined and the terms by degree in descending numerical order​

​

​This way we can find the leading coefficient

Multiple Choice

What is the leading coefficient in the polynomial 3x²-2x+5?

• 3
• 2
• 5
• 0

Multiple Choice

What id the Degree of the Polynomial?
5x³ - 6x + 1

• Linear 
• Quadratic
• Cubic
• Quartic

Multiple Choice

Classify by number of terms:
3x³ – 6x

• Monomial
• Binomial
• Trinomial
• 4-Term Polynomial

Multiple Choice

Classify by the DEGREE:
2x² - 5

• Degree of 1
• Degree of 2
• Degree of 3
• Degree of 4

Multiple Choice

Which polynomial is written in standard form?

• -3x + 8x² + 9x³ - 11
• 9x³ + 8x² - 3x - 11
• 8x² + 9x³ -11 - 3x
• -11 - 3x + 8x² + 9x³

Multiple Choice

Which of the following is a 5th degree trinomial with a leading coefficient of -2? 

• -2x⁵ + 3x - 1
• 5x^-2 +3x - 1
• -2x⁵ + 3x⁴ + 2x³ + x² - 10
• 2x + 5

Multiple Choice

3) Degree of

$$5a^4+7a^2-3a^9+10$$  is ____

• 2

• 4

• 9

• 10

Multiple Choice

Determine the solution to the given linear-quadratic function.

• No Solution

• (3, 0)

• (2, -3)

• (-3, 2)