3.4 Graphs of polynomial functions  (Page 8/13)

What is the difference between an $x\text{-}$ intercept and a zero of a polynomial function $f?$

If a polynomial function of degree $n$ has $n$ distinct zeros, what do you know about the graph of the function?

Explain how the Intermediate Value Theorem can assist us in finding a zero of a function.

Explain how the factored form of the polynomial helps us in graphing it.

If the graph of a polynomial just touches the $x\text{-}$ axis and then changes direction, what can we conclude about the factored form of the polynomial?

$C\left(t\right)=2\left(t-4\right)\left(t+1\right)(t-6)$

$C\left(t\right)=3\left(t+2\right)\left(t-3\right)(t+5)$

$C\left(t\right)=4t{\left(t-2\right)}^2(t+1)$

$C\left(t\right)=2t\left(t-3\right){\left(t+1\right)}^2$

$C\left(t\right)=2t^4-8t^3+6t^2$

$C\left(t\right)=4t^4+12t^3-40t^2$

$f(x)=x^4-x^2$

$f(x)=x^3+x^2-20x$

$f(x)=x^3+6x^2-7x$

$f(x)=x^3+x^2-4x-4$

$f(x)=x^3+2x^2-9x-18$

$f(x)=2x^3-x^2-8x+4$

$f(x)=x^6-7x^3-8$

$f(x)=2x^4+6x^2-8$

$f(x)=x^3-3x^2-x+3$

$f(x)=x^6-2x^4-3x^2$

$f(x)=x^6-3x^4-4x^2$