Graphing Polynomials

Presentation

•

Mathematics

•

12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSA.APR.B.3, HSA.CED.A.2, HSA.APR.A.1

Standards-aligned

Victoria Colbert

Used 35+ times

FREE Resource

8 Slides • 20 Questions

Graphing Polynomials

Algebra 2

Positive vs Negative

Functions with a POSITIVE leading coefficient - RIGHT end goes UP
Functions with a NEGATIVE leading coefficient - RIGHT end goes DOWN

Multiple Select

Which graphs have a POSITIVE leading coefficient? (Check all that apply)

Odd vs Even

Functions with an ODD degree - ends go in OPPOSITE directions
Functions with an EVEN degree - ends go in the SAME direction

Multiple Select

Which graphs have an ODD degree? (Check all that apply)

Multiple Choice

$\$ Which could be the graph of $f\left(x\right)=2x^3+3x^2+4\ ?$

Multiple Choice

$\$ Which could be the graph of $f\left(x\right)=-3x^8+17x^6-14x^3+2x^2-1\ ?$

Multiple Choice

$\$ Which could be the graph of $\ f\left(x\right)=-4x^5-19x^4+22x^2-x\ ?$

Factors & Zeros

If in factored form a polynomial

f(x) = (x-a)(x-b)(x-c), then

(x-a), (x-b), and (x-c) are "factors" and

a, b, and c are zeros - they are the x-intercepts of the graph found at points (a,0), (b,0), and (c,0).

*The zeros are the opposite of what you see in the parenthesis!

Multiple Choice

$\$ Which graph depicts the function $f\left(x\right)=\left(x-6\right)\left(x-3\right)\left(x+8\right)?$

Multiplicities (CBS)

Multiple Choice

$\$ Which graph depicts the function $f\left(x\right)=\left(x-2\right)^2\left(x-8\right)?$

Multiple Choice

$\$ Which graph depicts the equation $f\left(x\right)\ =x^2\left(x+4\right)^3\left(x-3\right)?$

Multiple Choice

Which is the equation for the graph shown?

$f\left(x\right)=x^3\left(x-5\right)^2$

$f\left(x\right)=x^2\left(x-5\right)$

$f\left(x\right)=x^3\left(x+5\right)^2$

$f\left(x\right)=x^2\left(x+5\right)^2$

End Behavior (Graphs)

Multiple Choice

Express the END BEHAVIOR of the graph shown.

x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty\

x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty

$x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$
$x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$

$x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$
$x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

$x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$
$x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

End Behavior (Equations)

Multiple Choice

Express the END BEHAVIOR of the function: $f\left(x\right)=-12x^7-19x^3+22$

$x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty\$

$x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$

$x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$ $x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$

$x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$ $x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

$x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$ $x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

Multiple Choice

Express the END BEHAVIOR of the function: $f\left(x\right)=7x^4+9x^3-21$

$x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty\$

$x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$

$x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$ $x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$

$x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$ $x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

$x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$ $x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

Multiple Choice

What is the degree of the function graphed here?

Multiple Choice

Which function is graphed?

(x - 4)(x + 2)(x - 8)=0

(x - 4)(x - 2)(x + 8)=0

(x - 4)(x + 2)(x + 8)=0

(x + 4)(x + 2)(x + 8)=0

Multiple Choice

What is the degree and end behaviors of the function behind this text? (As x−>∞, as x−>-∞, as usual...)

2; ∞,-∞

3; ∞,∞

4; ∞,∞

6; ∞,∞

Multiple Choice

What is the degree of the polynomial function
P(x)=3x⁴-7x²-2x⁷-x+4?

Multiple Choice

Describe the end behavior of
f(x) = -5x⁴ - 2x² + 8

Left side: Rises
Right side: Rises

Left Side: Rises
Right side: Falls

Left side: Falls
Right side: Rises

Left side: Falls
Right side: Falls

Multiple Choice

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient

Leading Coefficient Positive
Degree - Even

Leading Coefficient Positive
Degree - Odd

Leading Coefficient Negative
Degree - Even

Leading Coefficient Negative
Degree - Odd

Multiple Choice

Which solution has a multiplicity of 2?

-1

none of them do

Multiple Choice

What is the correct graph of the function?

Graphing Polynomials

Algebra 2

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