Analyzing zeros of polynomial graphs

Presentation

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSF-IF.C.7C, HSA.APR.B.3

Standards-aligned

Karine Ptak

Used 28+ times

FREE Resource

17 Slides • 3 Questions

Analyzing zeros of polynomial graphs

by Karine Ptak

PART 1

MULTIPLICITY

YOU SHOULD WRITE THIS DOWN...

Multiple Choice

If we follow the definition of multiplicity, $\left(x-1\right)^3=0$ would result in $x=1$ with a multiplicity of...

Keep writing...

Before we start... We use the following terms almost interchangeably. Although there are some distinctions, they represent more or less the same thing:

solutions, zeros, roots, and x-intercepts

Multiple Choice

What kind of multiplicity would the zeros of this graph have?

x=-1 has an odd multiplicity

x=2 has an odd multiplicity

x=-1 has an odd multiplicity

x=2 has an even multiplicity

x=-1 has an even multiplicity

x=2 has an odd multiplicity

x=-1 has an even multiplicity

x=2 has an even multiplicity

PART 2

The truth about imaginary zeros

When you learned about the discriminant...

We can use the discrimant to help us figure out the number and the nature of roots/zeros/solutions

IMAGINARY ROOTS/ZEROS...

... ALWAYS COME IN PAIRS

PART 3

The Fundamental Theorem of Algebra

The number of zeros of a polynomial function is equal to the degree of the polynomial function.

Make sure you understand the sentence above.

What that means:

Linear equation: degree is 1, one solution

Quadratic equation: degree is 2, two solutions

Cubic equation: degree is 3, three solutions

Get it? So, given that the graph on the right only has real solutions, what is the degree of the function?

These are the graphs of...

... quadratic functions. Each has two zeros. The green graph has two zeros; they just happen to be imaginary. The blue graph has two zeros, at x=-4 and x=3. The red graph has a zero at x=10, but its multiplicity is 2, so it counts as 2.

This is the graph of...

Fill in the Blanks

If you wanted to create a function from this graph that include imaginary solutions, what could be the degree of your function?

Type answer...

Analyzing zeros of polynomial graphs

by Karine Ptak

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