Maiclubk
2021-06-13
Answered

Find the quadratic polynomial whose graph passes through the points (0, 0), (-1, 1), and (1, 1).

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asked 2021-06-28

Every cubic polynomial can be categorised into one of four types: Type 1: Three real, distinct zeros:

Type 2: Two real zeros, one repeated:

Type 3: One real zero repeated three times:

Type 4: One real and two imaginary zeros:

Experiment with the graphs of Type 1 cubics. Clearly state the effect of changing both the size and sign of a. What is the geometrical significance of

asked 2021-08-01

Graph the polynomial by transforming an appropriate graph of the form $y={x}^{n}$ .

Show clearly all x- and y-intercepts.$P\left(x\right)=81-{(x-3)}^{4}$

Show clearly all x- and y-intercepts.

asked 2021-01-05

Let ${S}_{N}\left(x\right)=\frac{4}{\pi}\text{}\sum _{n=1}^{N}\text{}\frac{1\text{}-\text{}{(-1)}^{n}}{{n}^{3}}\text{}\mathrm{sin}\left(nx\right).$

Construct graphs of${S}_{N}\left(x\right)\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}x(\pi \text{}-\text{}x),\text{}f{\textstyle \phantom{\rule{1em}{0ex}}}\text{or}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}0\text{}\le \text{}x\text{}\le \text{}\pi ,\text{}f{\textstyle \phantom{\rule{1em}{0ex}}}\text{or}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}N=2\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}then\text{}N=10.$

This will give some sense of the correctness of Fourier’s claim that this polynomial could be exactly represented by the infinite series

$\frac{4}{\pi}\text{}\sum _{n=1}^{\mathrm{\infty}}\text{}\frac{1\text{}-\text{}{(-1)}^{n}}{{n}^{3}}\text{}\mathrm{sin}\left(nx\right)\text{}on\text{}[0,\text{}\pi ].$

Construct graphs of

This will give some sense of the correctness of Fourier’s claim that this polynomial could be exactly represented by the infinite series

asked 2020-10-28

Use the appropriate Lagrange interpolating polynomials to find the cubic polynomial whose graph passes through the given points.
$(2,\text{}1),\text{}(3,\text{}1),\text{}(4,\text{}-3),\text{}(5,\text{}0)$ .

asked 2021-06-08

For the following exercises, use the given information about the polynomial graph to write the equation. Degree 3. Zeros at

asked 2020-10-21

Solve the polynomial inequality graphically. $3{x}^{4}-5{x}^{3}-12{x}^{2}+12x+16$

asked 2021-08-02

Graph each polynomial function. $f\left(x\right)={x}^{4}+{x}^{3}-3{x}^{2}-x+2$