Objective 2 - Graph Polynomials

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Convert between a polynomial function and its graph.

Link to section in online textbook.

First, watch this video to learn what the different forms of a polynomial can tell you about its shape. Now practice converting between the graph and the corresponding equation.

Write an equation of the function graphed below.

List zeros from smallest to largest. Use $\sage {evenExp1}$ and $\sage {oddExp1}$ as exponents. The leading coefficient is either $1$ or $-1$ .

$f(x) = \answer {1}(x - \answer {0})^{\answer {\sage {oddExp1}}}(x - \answer {1})^{\answer {\sage {oddExp1}}}(x - \answer {2})^{\answer {\sage {oddExp1}}}$

Write an equation of the function graphed below.

List zeros from smallest to largest. Use $\sage {evenExp2}$ and $\sage {oddExp2}$ as exponents. The leading coefficient is either $1$ or $-1$ .

$f(x) = \answer {-1}(x - \answer {-1})^{\answer {\sage {oddExp2}}}(x - \answer {0})^{\answer {\sage {oddExp2}}}(x - \answer {2})^{\answer {\sage {oddExp2}}}$

Write an equation of the function graphed below.

List zeros from smallest to largest. Use $\sage {evenExp3}$ and $\sage {oddExp3}$ as exponents. The leading coefficient is either $1$ or $-1$ .

$f(x) = \answer {-1}(x - \answer {-1})^{\answer {\sage {evenExp3}}}(x - \answer {1})^{\answer {\sage {evenExp3}}}(x - \answer {2})^{\answer {\sage {evenExp3}}}$

Write an equation of the function graphed below.

List zeros from smallest to largest. Use $\sage {evenExp4}$ and $\sage {oddExp4}$ as exponents. The leading coefficient is either $1$ or $-1$ .

$f(x) = \answer {1}(x - \answer {-3})^{\answer {\sage {oddExp4}}}(x - \answer {1})^{\answer {\sage {oddExp4}}}(x - \answer {2})^{\answer {\sage {evenExp4}}}$

Press...	...to do
left/right arrows	Move cursor
shift+left/right arrows	Select region
ctrl+a	Select all
ctrl+x/c/v	Cut/copy/paste
ctrl+z/y	Undo/redo
ctrl+left/right	Add entry to list or column to matrix
shift+ctrl+left/right	Add copy of current entry/column to to list/matrix
ctrl+up/down	Add row to matrix
shift+ctrl+up/down	Add copy of current row to matrix
ctrl+backspace	Delete current entry in list or column in matrix
ctrl+shift+backspace	Delete current row in matrix

Type...	...to get
norm	$\|\|\blue{[?]}\|\|$
text	$\text{\blue{[?]}}$
sym_name	$\backslash\texttt{\blue{[?]}}$
abs	$\left\|\blue{[?]}\right\|$
sqrt	$\sqrt{\blue{[?]}}$
paren	$\left(\blue{[?]}\right)$
floor	$\lfloor \blue{[?]} \rfloor$
factorial	$\blue{[?]}!$
exp	${\blue{[?]}}^{\blue{[?]}}$
sub	${\blue{[?]}}_{\blue{[?]}}$
frac	$\dfrac{\blue{[?]}}{\blue{[?]}}$
int	$\displaystyle\int{\blue{[?]}}d\blue{[?]}$
defi	$\displaystyle\int_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}d\blue{[?]}$
deriv	$\displaystyle\frac{d}{d\blue{[?]}}\blue{[?]}$
sum	$\displaystyle\sum_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}$
prod	$\displaystyle\prod_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}$
root	$\sqrt[\blue{[?]}]{\blue{[?]}}$
vec	$\left\langle \blue{[?]} \right\rangle$
mat	$\left(\begin{matrix} \blue{[?]} \end{matrix}\right)$
*	$\cdot$
infinity	$\infty$
arcsin	$\arcsin\left(\blue{[?]}\right)$
arccos	$\arccos\left(\blue{[?]}\right)$
arctan	$\arctan\left(\blue{[?]}\right)$
sin	$\sin\left(\blue{[?]}\right)$
cos	$\cos\left(\blue{[?]}\right)$
tan	$\tan\left(\blue{[?]}\right)$
sec	$\sec\left(\blue{[?]}\right)$
csc	$\csc\left(\blue{[?]}\right)$
cot	$\cot\left(\blue{[?]}\right)$
log	$\log\left(\blue{[?]}\right)$
ln	$\ln\left(\blue{[?]}\right)$
alpha	$\alpha$
beta	$\beta$
gamma	$\gamma$
delta	$\delta$
epsilon	$\epsilon$
zeta	$\zeta$
eta	$\eta$
theta	$\theta$
iota	$\iota$
kappa	$\kappa$
lambda	$\lambda$
mu	$\mu$
nu	$\nu$
xi	$\xi$
omicron	$\omicron$
pi	$\pi$
rho	$\rho$
sigma	$\sigma$
tau	$\tau$
upsilon	$\upsilon$
phi	$\phi$
chi	$\chi$
psi	$\psi$
omega	$\omega$
Gamma	$\Gamma$
Delta	$\Delta$
Theta	$\Theta$
Lambda	$\Lambda$
Xi	$\Xi$
Pi	$\Pi$
Sigma	$\Sigma$
Phi	$\Phi$
Psi	$\Psi$
Omega	$\Omega$

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