Math 3 Unit 4 Day 2...
Transcript of Math 3 Unit 4 Day 2...
Math 3 Unit 4 Day 2 Notes.notebook October 20, 2015
Polynomial Functions
Unit 4 Day 2 from intercepts
Math 3 Unit 4 Day 2 Notes.notebook October 20, 2015
Desmos Activity RecapThe factors of a polynomial function tells us its x-intercepts.
x-intecepts happen when y = 0 (For which x does f(x)=0?)
standard form
intercept form
x-intercepts
roots of the equation zeros of the function{
Math 3 Unit 4 Day 2 Notes.notebook October 20, 2015
Some factors in a function have multiplicity.The multiplicity of a factor is how many times that factor appears in a polynomial.
standard form
intercept form
roots/zeros
x-intercepts
{multiplicity 2 multiplicity 3
Math 3 Unit 4 Day 2 Notes.notebook October 20, 2015
multiplicity graph behavior examples
even touch
odd cross
Math 3 Unit 4 Day 2 Notes.notebook October 20, 2015
The Fundamental Theorem of AlgebraA polynomial equation of degree n has exactly n roots in the set of complex numbers, including repeated roots.
• We know how many roots a polynomial has.
• If a polynomial is factorable, we can find the roots by factoring.
• If we graph the function, we can see the real roots they correspond to the xintercepts.
Implications:
(We'll work with factoring again next time. Yay!)
(Imaginary roots are not revealed by graphing... more about that later.)
(The degree tells us how many!)
Math 3 Unit 4 Day 2 Notes.notebook October 20, 2015
If I give you the roots (or show you a picture of the graph), can you find an equaon for the polynomial?
By the end of class, for sure!
Today's big thing:
Math 3 Unit 4 Day 2 Notes.notebook October 20, 2015
Example 1: Write a cubic polynomial function that has zeros 1, 2, and 3.
Math 3 Unit 4 Day 2 Notes.notebook October 20, 2015
Look at the graph in Desmos...
https://www.desmos.com/calculator/rdqdizvl37
Math 3 Unit 4 Day 2 Notes.notebook October 20, 2015
Example 2: Write an equation for the cubic polynomial shown. (both intercept and standard forms...)
Intercept Form:
Standard Form:
Factors:Multiply:
check y-intercept:
x-intercepts:
Math 3 Unit 4 Day 2 Notes.notebook October 20, 2015
Example 3: The three roots of cubic polynomial function f(x) are 0 and 3 with multiplicity 2. The function has a leading coefficient of 1/3. What is f(x)?
Math 3 Unit 4 Day 2 Notes.notebook October 20, 2015
Example 4: Write an equation for the cubic function shown.
Math 3 Unit 4 Day 2 Notes.notebook October 20, 2015
Practice A: Write a polynomial function that has zeros 1, 3, and 5.
Math 3 Unit 4 Day 2 Notes.notebook October 20, 2015
Practice B: Write an equation (in standard form)for the cubic polynomial shown.
Math 3 Unit 4 Day 2 Notes.notebook October 20, 2015
Practice C: Cubic function g(x) has two unique roots: 2 (mult. 1) and 1 (mult. 2). Function g(x) has a yintercept of 1/2. What is the standard form of g(x)?
Math 3 Unit 4 Day 2 Notes.notebook October 20, 2015
Practice D: Write an equation for a quartic polynomial with zeros at 2, 0, 3, and 4.
• What is the y-intercept of your function?
Math 3 Unit 4 Day 2 Notes.notebook October 20, 2015