Polynomial Equations and Graphs: Discover the Relationship

High School
Algebra
Algebra II
Polynomial graphs

$f (x) = 100 {(1.25)}^{x}$
Is it true or false, the growth factor is 25%? If not, what is and what is 25%?

ossidianaZ 2021-08-14

$(\frac{2}{7}, - 1) and 9 + \frac{1}{3 i}$ are zeros.
Find a polynomial function with real coefficients.

CoormaBak9 2021-08-11

$y = x^{3} - 2 x^{2} - x + 2$
and $y = - x^{2} + 5 x + 2$
To determine:a) Graph of both functions
b) At how many points do the both graphs appear to intersect.
c) Find coordinates of all intersection points

EunoR 2021-08-10

$f (x) = x^{5} + 2 x^{4} + 3 x^{3} - 2 x^{6} - 9 x^{2} - 6 x + 4$
Is it true or false the degree of this polynomial function is 5? If not, why? What is the degree?

Emily-Jane Bray 2021-08-10

Determine whether the statement is true or false.
If it is false, explain why or give an example that shows it is false.
The graphs of polynomial functions have no vertical asymptotes.

Rivka Thorpe 2021-08-02

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

texelaare 2021-08-02

Investigate the change in the graph of a sinusoidal function of the form $and = \sin x$ or $and = \cos x$ when multiplied by a polynomial function. Use a graphing calculator to sketch the graphs of $and = x^{2}, and = - x^{2}$ and $and = x^{2} \sin x$ on the same coordinate plane, on the interval [-20, 20].

Armorikam 2021-08-01

Graph the polynomial by transforming an appropriate graph of the form $y = x^{n}$ .
Show clearly all x- and y-intercepts. $P (x) = 81 - {(x - 3)}^{4}$

FizeauV 2021-07-20

The values of two functions, f and g, are given in a table. One, both, or neither of them may be exponential. Decide which, if any, are exponential, and give the exponential models for those that are.
$\begin{matrix} x & - 2 & - 1 & 0 & 1 & 2 \\ f (x) & 0.8 & 0.2 & 0.1 & 0.005 & 0.025 \\ g (x) & 80 & 40 & 20 & 10 & 2 \end{matrix}$

preprekomW 2021-06-28

Every cubic polynomial can be categorised into one of four types: Type 1: Three real, distinct zeros: $P (x) = a (x - α) (x - β) (x - γ), a \neq 0$
Type 2: Two real zeros, one repeated: $P (x) = a (x - α) 2 (x - β), a \neq 0$
Type 3: One real zero repeated three times: $P (x) = a (x - α) 3, a \neq 0$
Type 4: One real and two imaginary zeros: $P (x) = (x - α) (a x 2 + b x + c), Δ = b 2 - 4 a c < 0, a \neq 0$
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 $α, β, a n d γ ? α, β, a n d γ$ ?

Brittney Lord 2021-06-25

For the following exercises, use the given information about the polynomial graph to write the equation. Degree 5. Double zero at $x = 1$ , and triple zero at $x = 3$ . Passes through the point (2, 15).

sjeikdom0 2021-06-20

How does one find the lovely asymptotes of a polynomial graph?

Phoebe 2021-06-20

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 $x = m i n u s$ ;2. y-intercept at (0, minus;3).

pancha3 2021-06-20

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)

babeeb0oL 2021-06-14

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.
$f (x) = 2 x^{2} - 3 x - 5$

Maiclubk 2021-06-13

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

Annette Arroyo 2021-06-13

Carla is using the Rational Root Theorem and synthetic division to find real roots of polynomial functions and sketch their graphs. She says she has wasted her time when she tests a possible root and finds a nonzero remainder instead. Do you agree with her statement? Explain your reasoning.

Daniaal Sanchez 2021-06-08

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 $(0, - 4)$ .

sibuzwaW 2021-06-07

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.
$f (x) = x^{3} + 3 x^{2} - x - 3$

Efan Halliday 2021-05-31

How can proficiency in factoring help when graphing polynomial functions without using a calculator?

If you are looking for polynomial graphs examples, do not forget about word problems as well because these will help you explain your questions that are dealing with polynomial problems. Always start with the composition of the graph and only then continue with the transformation of variables or the use of an equation like in the case with polynomial equations and graphs. See some examples below and approach them the same way with a detailed analysis. If you need to start with your polynomial graph to equation homework, these samples with answers will be essential.

Algebra II

Polynomial Graphs Examples: See the Power of Polynomials in Action