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).

iohanetc 2021-03-08 Answered
For the following exercises, use the given information about the polynomial graph to write the equation. Double zero at x=3 and triple zero atx=0. Passes through the point (1, 32).
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

BleabyinfibiaG
Answered 2021-03-09 Author has 118 answers
Step 1 Data: x-intercept of multiplicity 2=3 x-intercept of multiplicity 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: f(x)=a(x+3)2(x0) Simplify: f(x)=ax3(x+3)2 In order to evaluate a, use the point on the graph (1,32), therefore substitute f(1)=32 in this equation: 32=a(1)3(1+3)2 Simplify: 32=a(1)(16)=16a Evaluate a: a=3216=2 This implies that the equation of the polynomial function is f(x)=2x3(x+3)2 Answer: The equation of the polynomial function is f(x)=2x3(x+3)2
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-06-22

Copy and complete the anticipation guide in your notes. StatementThe quadratic formula can only be used when solving a quadratic equation.Cubic equations always have three real roots.The graph of a cubic function always passes through all four quadrants.The graphs of all polynomial functions must pass through at least two quadrants.The expression x2>4 is only true if x>2.If you know the instantaneous rates of change for a function at x=2 and x=3, you can predict fairly well what the function looks like in between.
Agree Disagree Justification
Statement
The quadratic formula can only be used when solving a quadratic equation. Cubic equations always have three real roots. The graph of a cubic function always passes through all four quadrants. The graphs of all polynomial functions must pass through at least two quadrants.
The expression x2>4 is only true if x>2. If you know the instantaneous rates of change for a function at x=2 and x=3, you can predict fairly well what the function looks like in between.

asked 2021-08-21
Find a nonzero polymonial function. The given zeros are:
a) 0, 1, 9
b) -3, -1, 0, 1, 3
asked 2021-06-20
How does one find the lovely asymptotes of a polynomial graph?
asked 2021-05-21

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

asked 2021-05-05

Every cubic polynomial can be categorised into one of four types: Type 1: Three real, distinct zeros: P(x)=a(xα)(xβ)(xγ),a0
Type 2: Two real zeros, one repeated: P(x)=a(xα)2(xβ),a0
Type 3: One real zero repeated three times: P(x)=a(xα)3,a0

Type 4: One real and two imaginary zeros: P(x)=(xα)(ax2+bx+c),=b24ac<0,a0
Experiment with the graphs of Type 4 cubics. What is the geometrical significance of αα and the quadratic factor which has imaginary zeros?

asked 2021-05-09
Graph the polynomial by transforming an appropriate graph of the form y=xn. Show clearly all x- and y-intercepts. P(x)=3(x+2)5+96
asked 2021-08-02
Graph each polynomial function. f(x)=x4+x33x2x+2