Graphing Polynomials

Presentation

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Mathematics

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11th Grade

•

Practice Problem

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Medium

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CCSS

HSA.APR.B.3, HSA.REI.D.10, HSF.IF.B.4

Standards-aligned

Khaliah Jones

Used 1K+ times

FREE Resource

8 Slides • 12 Questions

Graphing Polynomials

Advanced Algebra

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)

MULTIPLCITY: $\rightarrow$ ACTION:
ONE $\rightarrow$ CUT through
Two (or any EVEN) $\rightarrow$ BOUNCE
ODD (Any odd 3+) $\rightarrow$ SQUIGGLE

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)

The END BEHAVIOR of a function f describes the behavior of the graph of the function at the "ends" of the x-axis.

x\rightarrow\infty

as we look to the RIGHT

x\rightarrow-\infty

as we look to the LEFT

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

the graph goes UP

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

the graph goes DOWN

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)

$x\rightarrow\infty$ , $f\left(x\right)\rightarrow$ +/- L.C.
$x\rightarrow-\infty$ , $f\left(x\right)\rightarrow$ Even/Odd Deg

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

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

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

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

Graphing Polynomials

Advanced Algebra

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