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Catherine Gospodarek » Integrated Math 3

Integrated Math 3

Welcome to Integrated Math 3!  This year we will work together to master concepts both old and new.  Integrated Math 3 is a new math course in Rutherford County that covers Algebra 2, Geometry, and Pre-Calculus.  There is a lot of material to cover but I am confident we can navigate these waters together, building knowledge and mastery along the way.  
 
To stay in contact throughout the year, I use the Remind app.  Reminders and updates will be posted several times per week.  To join my Remind, please text @4ceef2 to 81010.  
 

Recent Posts

Average Rate of Change

The average rate of change of a polynomial can be found using the same formula that we use for slope.  We are simply looking for the change in y-values divided by the change in x-values.  This comes in handy when we look at real-life scenarios.  Within a given interval, you are to calculate the average rate of change.  This is our secant line of the curve.  Worksheet assignment for Friday, November 2 follows.  

Mrs. Jones

As many of you are aware, Mrs. Jones, an Integrated Math II teacher here at Riverdale, whom many of my students had as their teacher last year, suffered an extreme tragedy last week.
 
Her husband was working on an elevator and lost his life when the pulley system broke and the counterweight struck him.
 
She and her husband, Daniel, were both Riverdale grads in 2010.  They have an eighteen month old daughter and she is seven months pregnant with their second daughter.
 
If you are interested in helping out her family financially, please contribute via the Go Fund Me page.
 
 
 

Polynomials

Fundamental Theorem of Algebra:   

  • Any polynomial of degree n has n roots.   
  • So a fourth degree polynomial has 4 roots; a second degree polynomial has 2 roots, etc.   

**Remember, a root is the same as a zero or an x-intercept. Roots can be real or imaginary!!!  

**The degree of a polynomial is determined by its highest degree exponent when a function is written in standard form (i.e. fx= ax2+bx+c).  If a function is not written in standard form (i.e. fx=(x−r1)(x−r2)(x−r3)), the x’s must be multiplied together to find the highest degree first.   

**The y-intercept of a polynomial function will be the “c” value or the number that does NOT have an x attached to it.   

Determine for each of the following polynomials: 

  1. Degree AND number of roots 
  1. End Behavior 
  1.  Y-intercept 
  • fx= 4x3+2x−1 
  • fx=x2−4x2+4 
  • fx=(x+3)(x−2)(x+1) 

 

 

 

 

September 5, 2018 

Number of Extrema can easily be found if you identify the degree of the function.  The number of extrema is always AT MOST one less than the degree of the function.   

  • A fourth-degree function can have at most three extrema. 
  • A second-degree function can have at most one extrema.   
  • The POSSIBLE number of extrema always goes down by two. 
  • For example, a fourth-degree function can have at most three extrema, but it could also have only one extrema.  A fifth-degree function can have at most four extrema, but it could also have two OR zero extrema.   

Determine the degree and POSSIBLE number of extrema for each of the following:  

  • 𝒇𝒙=𝟐𝒙𝟓−𝟒𝒙+𝟑 
  • 𝒇𝒙=𝟑𝒙−𝟒𝒙𝟑−𝟖𝒙𝟐−𝟗 
  • 𝒇𝒙=𝟐𝒙(𝒙𝟑+𝟒)