# Graph each polynomial function.f(x)=2x^{3} - x^{2} + 2x - 1 PSZ

Question
Polynomial graphs

Graph each polynomial function. $$f(x)=2x^{3}\ -\ x^{2}\ +\ 2x\ -\ 1$$

2021-02-04

### Relevant Questions

(a) find the Maclaurin polynomial $$\displaystyle{P}_{{{3}}}{\left({x}\right)}$$ for PSKf(x), (b) complete the following

$$\begin{array}{|c|c|}\hline x: & -0.75 & -0.50 & -0.25 & 0 & 0.25 & 0.50 & 0.75 \\ \hline \end{array}$$

for f(x) and $$P_{3}(x)$$ and (c) sketch the graphs of f(x) and $$\displaystyle{P}_{{{3}}}{\left({x}\right)}$$ on the same set of coordinate axes. $$\displaystyle{f{{\left({x}\right)}}}={\arctan{{x}}}$$

Graph each polynomial function. Factor first if the expression is not in factored form. $$f(x)=x^{3}\ +\ 3x^{2}\ -\ 13x\ -\ 15$$

Simplify each expression.
1) $$-n+9n+3-8-8n$$
2) $$3(-4x+5y)-3x(2+4)$$
3) $$5-4y+x+9y$$
4) $$-2x+3y-5x-(-8y)$$

Nested Form of a Polynomial Expand Q to prove that the polynomials P and Q ae the same $$\displaystyle{P}{\left({x}\right)}={3}{x}^{{4}}-{5}{x}^{{3}}+{x}^{{2}}-{3}{x}+{5}\ {Q}{\left({x}\right)}={\left({\left({\left({3}{x}-{5}\right)}{x}+{1}\right)}{x}-{3}\right)}{x}+{5}$$ Try to evaluate P(2) and Q(2) in your head, using the forms given. Which is easier? Now write the polynomial $$\displaystyle{R}{\left({x}\right)}={x}^{{5}}—{2}{x}^{{4}}+{3}{x}^{{3}}—{2}{x}^{{3}}+{3}{x}+{4}$$ in “nested” form, like the polynomial Q. Use the nested form to find R(3) in your head. Do you see how calculating with the nested form follows the same arithmetic steps as calculating the value ofa polynomial using synthetic division?

Polynomial equation with real coefficients that has the roots $$3, 1 -i\ \text{is}\ x^{3} - 5x^{2} + 8x - 6 = 0.$$

What is the process to solve these:
Vertex, $$y-\int$$., $$x-\int$$, graph $$= -(x+1)^2+1$$

Describe the relationship between the two quantities.

A graph of a linear equation passes through ( -2,0) and (0,-6) is the $$3x-y=6$$, both ordered pairs solutions for the equation

Solve linear equation and check: $$7x+3=6(x-1)+9$$

Determine the value of k for which the point (- 2, 3) lies on the line whose equation is .

$$4x+3ky=10$$

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