Ask question

# For the following exercises, use the given information about the polynomial graph to write the equation. Double zero at x = −3 and triple zero at x = 0. Passes through the point (1, 32). # For the following exercises, use the given information about the polynomial graph to write the equation. Double zero at x = −3 and triple zero at x = 0. Passes through the point (1, 32).

Question
Polynomial graphs asked 2021-03-08
For the following exercises, use the given information about the polynomial graph to write the equation. Double zero at $$\displaystyle{x}=−{3}$$ and triple zero $$\displaystyle{a}{t}{x}={0}$$. Passes through the point (1, 32).

## Answers (1) 2021-03-09
Step 1 Data: x-intercept of multiplicity $$\displaystyle{2}=-{3}$$ x-intercept of multiplicity $$\displaystyle{3}={0}$$ Degree =5 Step 2 Since it is a fifth degree polynomial function with multiplicity of 2 and 3 for some zeros, its general equation becomes: $$\displaystyle{f{{\left({x}\right)}}}={a}{\left({x}+{3}\right)}^{{{2}}}{\left({x}-{0}\right)}$$ Simplify: $$\displaystyle{f{{\left({x}\right)}}}={a}{x}^{{{3}}}{\left({x}+{3}\right)}^{{{2}}}$$ In order to evaluate a, use the point on the graph (1,32), therefore substitute $$\displaystyle{f{{\left({1}\right)}}}={32}$$ in this equation: $$\displaystyle{32}={a}{\left({1}\right)}^{{{3}}}{\left({1}+{3}\right)}^{{{2}}}$$ Simplify: $$\displaystyle{32}={a}{\left({1}\right)}{\left({16}\right)}={16}{a}$$ Evaluate a: $$\displaystyle{a}={\frac{{{32}}}{{{16}}}}={2}$$ This implies that the equation of the polynomial function is $$\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{{3}}}{\left({x}+{3}\right)}^{{{2}}}$$ Answer: The equation of the polynomial function is $$\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{{3}}}{\left({x}+{3}\right)}^{{{2}}}$$

### Relevant Questions asked 2021-05-14
For the equation (-1,2), $$y= \frac{1}{2}x - 3$$, write an equation in slope intercept form for the line that passes through the given point and is parallel to the graph of the given equation. asked 2021-06-02
Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form.
Passing through (3,-1) and perpendicular to the line whose equation is x-9y-5=0
Write an equation for the line in point-slope form and slope-intercept form. asked 2020-10-28
Use the appropriate Lagrange interpolating polynomials to find the cubic polynomial whose graph passes through the given points. $$\displaystyle{\left({2},\ {1}\right)},\ {\left({3},\ {1}\right)},\ {\left({4},\ −{3}\right)},\ {\left({5},\ {0}\right)}$$. asked 2021-05-16
Consider the curves in the first quadrant that have equationsy=Aexp(7x), where A is a positive constant. Different valuesof A give different curves. The curves form a family,F. Let P=(6,6). Let C be the number of the family Fthat goes through P.
A. Let y=f(x) be the equation of C. Find f(x).
B. Find the slope at P of the tangent to C.
C. A curve D is a perpendicular to C at P. What is the slope of thetangent to D at the point P?
D. Give a formula g(y) for the slope at (x,y) of the member of Fthat goes through (x,y). The formula should not involve A orx.
E. A curve which at each of its points is perpendicular to themember of the family F that goes through that point is called anorthogonal trajectory of F. Each orthogonal trajectory to Fsatisfies the differential equation dy/dx = -1/g(y), where g(y) isthe answer to part D.
Find a function of h(y) such that x=h(y) is the equation of theorthogonal trajectory to F that passes through the point P. asked 2021-05-27
Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form.
Passing through (-2,-8) and parallel to the line whose equation is y=-3x+4
Write an equation for the line in point-slope form and slope-intercept form. asked 2020-11-09
Use the appropriate Lagrange interpolating polynomials to find the cubic polynomial whose graph passes through the given points. $$\displaystyle{\left({1},{2}\right)},{\left({2},{1}\right)},{\left({3},{3}\right)},{\left({6},{1}\right)}{\left({1},{2}\right)},{\left({2},{1}\right)},{\left({3},{3}\right)},{\left({6},{1}\right)}$$. asked 2021-02-23
A 0.30 kg ladle sliding on a horizontal frictionless surface isattached to one end of a horizontal spring (k = 500 N/m) whoseother end is fixed. The ladle has a kinetic energy of 10 J as itpasses through its equilibrium position (the point at which thespring force is zero).
(a) At what rate is the spring doing work on the ladle as the ladlepasses through its equilibrium position?
(b) At what rate is the spring doing work on the ladle when thespring is compressed 0.10 m and the ladle is moving away from theequilibrium position? asked 2020-12-03

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 asked 2021-06-03
For the equation, a. Write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation.
$$4/(x + 5) + 2/(x - 5) = 32/(x^{2} - 25)$$ asked 2021-02-14
Find the cubic polynomial whose graph passes through the points $$\displaystyle{\left(-{1},-{1}\right)},{\left({0},{1}\right)},{\left({1},{3}\right)},{\left({4},-{1}\right)}.$$
...