High school polynomial graphs problems, solved and explained

Recent questions in Polynomial graphs

Jewel Beard 2022-04-09 Answered

Use the table method to find the quotient.
Then, substitute the value $y = 2$ into eachpolynomial, and show that the polynomialsrepresent integers with a true division equation.Show your work for both tasks!
$(\frac{12 y^{4} + 4 y^{3} - 31 y^{2} - 9 y + 9}{4 y^{2} - 9})$

Aarav Rangel 2022-02-04 Answered

Fill in the blank/s.:True or false - Even-degree polynomial functions have graphs with the same behavior at each end ____________

Anabelle Schneider 2022-02-01 Answered

Consider the polynomial function $g (x) = - x^{5} - 9 x^{3} - 8 x .$ Factor $g (x)$ completely and determine all of its complex zeros. Which of the zeros of g are not x-intercepts of the graph of $y = g (x) ?$ Why do these zeros not correspond to a point on the x-axis? In general, what can be said about the similarities and differences between the zeros and the x-intercepts of the graphs of polynomial functions?

toofehblf 2022-02-01 Answered

The behavior of the graph of a polynomial function to the far left or the far right is called its_ behavior, which depends upon the_ term.

Emerson Barnes 2022-01-31 Answered

6.When a polynomial $x 4 + x 3 - 10 x 2 - 1$ is divided by another polynomial, the quotient is $x 3 - 3 x 2 + 2 x - 8$ and the remainder is 31. Find the other polynomial.
Please type the answer, not in writing thank you

joygielymmeloiy 2022-01-31 Answered

1. Is $x^{2} - 2 \sqrt{5} x + x$ a polynomial? If not, state a reason.
2. Is -2020x a polynomial? If not, state a reason.
3. Is $x \frac{2}{3} + 3 x + 1$ a polynomial? If not, state a reason.
4. Is $\frac{1}{x^{2}} + \frac{r}{x^{3}} + \frac{r}{x^{4}}$ a polynomial? If not, state a reason.
5. Is $π$ a polynomial? If not, state a reason.
6. Is $x 3^{\sqrt{2}} + c h e c k m a r k 3 x^{2}$ a polynomial? If not, state a reason.
7. Is $x^{3} + 2 x + 1$ a polynomial? If not, state a reason.
8. Is $- 2 x^{- 3} + x^{3}$ a polynomial? If not, state a reason.
9. Is $1 - 4 x^{2}$ a polynomial? If not, state a reason.

William Curry 2021-12-24 Answered

How to find the end behavior of a quadratic function?

mronjo7n 2021-11-22 Answered

a) By inspection, find a particular solution of
$y + 2 y = 10$
b) By inspection, find a particular solution of
$y + 2 y = - 4 x$
c) Find a particular solution of
$y + 2 y = - 4 x + 10$
d) Find a particular solution of
$y + 2 y = 8 x + 5$

dictetzqh 2021-11-20 Answered

Summarize how graphs can be used to find solutions to polynomial inequalities.

xcl3411 2021-11-19 Answered

Find the exact length of the curve.
$x = e^{t} + e^{- t}, y = 5 - 2 t, 0 \leq t \leq 3$

ikavumacj 2021-11-16 Answered

Taylor’s formula with $n = 1$ and $a = 0$ gives the linearization of a function at $x = 0$ With $n = 2$ and $n = 3$ we obtain the standard quadratic and cubic approximations. In these exercises we explore the errors associated with these approximations. We seek answers to two questions:
a) For what values of x can the function be replaced by each approximation with an error less than $10^{- 2}$
b. What is the maximum error we could expect if we replace the function by each approximation over the specified interval? Using a CAS, perform the following steps to aid in answering questions (a) and (b) for the functions and interval.
Step 1: Plot the function over the specified interval.
Step 2: Find the Taylor polynomials $P_{1} (x), P_{2} (x) and P_{3} (x)$ at $x = 0$
Step 3: Calculate the $(n + 1)$ st derivative $f^{(n + 1)} (c)$ associated with the remainder term for each Taylor polynomial. Plot the derivative as a function of c over the specified interval and estimate its maximum absolute value, M.
Step 4: Calculate the remainder $R_{n} (x)$ for each polynomial. Using the estimate M from Step 3 in place of $f_{(n + 1)} (c)$ plot $R_{n} (x)$ over the specified interval. Then estimate the values of x that answer question (a).
Step 5: Compare your estimated error with the actual error $E_{n} (x) = | f (x) - P_{n} (x) |$ by plotting $E_{n} (x)$ over the specified interval. This will help answer question (b).
Step 6: Graph the function and its three Taylor approximations together. Discuss the graphs in relation to the information discovered in Steps 4 and 5.
$f (x) = {(1 + x)}^{\frac{3}{2}}, - \frac{1}{2} \leq x \leq 2$

Emily-Jane Bray 2021-10-27 Answered

Use Definition 2 to find an expression for the area under the graph of f as a limit. Do not evaluate the limit. $f (x) = x^{2} + {(1 + 2 x)}^{\frac{1}{2}}, 4 \leq x \leq 7$

nitraiddQ 2021-10-26 Answered

Do you agree with the contention that the functions f(x) = x + 2 and g(x) = x 2 − 4 x – 2are the same in every respect. Provide evidence to support your position.

Khaleesi Herbert 2021-10-23 Answered

Previously, you have approximated curves with the graphs of Taylor polynomials. Discuss possible circumstances in which the osculating circle would be a better or worse approximation of a curve than the graph of a polynomial.

postillan4 2021-09-30 Answered

For the following exercises, use the given information about the polynomial graph to write the equation. Degree 3. Zeros at x = −2, x = 1, and x = 3. y-intercept at (0, −4).

Suman Cole 2021-09-28 Answered

For the following exercises, use the given information about the polynomial graph to write the equation. Degree 5. Roots of multiplicity 2 at x = 3 and x = 1, and a root of multiplicity 1 at x = −3. y-intercept at (0, 9)

alesterp 2021-09-26 Answered

For the following exercises, use the given information about the polynomial graph to write the equation. Degree 3. Zeros at x = −5, x = −2, and x = 1. y-intercept at (0, 6)

necessaryh 2021-09-25 Answered

For the following exercise, for each polynomial, a. find the degree. b. find the zeros, if any. c. find the y-intercept(s), if any. d. use the leading coefficient to determine the graph’s end behavior. and e. determine algebraically whether the polynomial is even, odd, or neither.
$f (x) = - 3 x^{2} + 6 x$

BenoguigoliB 2021-09-24 Answered

For the following exercises, use the given information about the polynomial graph to write the equation. Degree 4. Root of multiplicity 2 at x = 4, and roots of multiplicity 1 at x = 1 and x = −2. y-intercept at (0, −3).

Aneeka Hunt 2021-09-24 Answered

For the following exercises, use the given information about the polynomial graph to write the equation. Degree 5. Roots of multiplicity 2 at x = −3 and x = 2 and a root of multiplicity 1 at x=−2. y-intercept at (0, 4).

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