Category: Algebra II

8/28/23 – Three Tips to Turn Polynomials into Graphs

Summary: Today we learned about how to tell certain characteristics of a graph given its polynomial function.

  1. Rule #1
    • Negative Leading Coefficient -> Right arm goes down.
    • Positive Leading Coefficient -> Right arm goes up.
  2. Rule #2
    • Odd Degree Polynomial -> Opposite End Behavior
    • Even Degree Polynomial -> Same End Behavior
  3. Rule #3
    • The number of bumps is less than the degree

See some examples below…

Homework: none

8/26/24 – Polynomial Vocabulary

Summary: Today we started by playing find the difference, find the mistake, and which one doesn’t belong.

We then took notes on the following polynomial vocabulary…

  • Polynomial – An expression with no variables in the denominator.
    • examples: 2x3-5x+9 or 0.5x-8
  • Terms – Expressions starting with + or –
    • example: 2x3-5x+9 has three terms
  • Exponent – The small number up top.
    • example: 2x3 has an exponent of 3
    • example: x has an exponent of invisible 1
  • Degree of a term – The exponent of the variable of a term.
    • example: -⅔x5 has a degree of five.
    • example: 83x has a degree of one (invisible)
    • example: 94  has a degree of 0 because there is no x.
  • Degree of a Polynomial – The largest degree.
    • example: 6x2-0.5x+7x6 has a degree of six.
    • example: -8x+99 has a degree of one (invisible)
  • Standard Form – A polynomial with terms arranged from highest degree to lowest degree.
    • example: 2x6+9x2-0.5x
  • Coefficient – The number in front of the variable.
    • example: 8x3 has a coefficient of eight.
    • example: x3 has a coefficient of one (invisible)
  • Leading Coefficient – the coefficient of the highest degree term.
    • example: 8x4-3x6-0.5x has a leading coefficient of -3.
  • Leading Term – The term with the highest degree
    • example: 8x4-3x6-0.5x has a leading term of -3x6
  • Constant – The degree zero term (just a number)
    • example: 8x4-3-0.5x has a constant of -3

Homework: none

8/21/24 – Introduction to Functions

Summary: Today we learned about function notation. We practice Algebra 1 multistep equations. We also practiced using our calculators. Below are some recommended calculators for iPhone and Android that are better than the default calculators.

Homework: HW03 Plotting and Graphing (Make sure your x-axis counts by 0.5, and your y-axis counts by 1, just like in the picture). Plug in x values to get the output f(x) values. Then plot the points, and connect the points to sketch the graph. (blank graph sheet to print)