Graphing Polynomials

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\$$

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

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

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

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