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NY Regents Algebra II Graphs of Polynomial Functions — practice questions

Explore 5 free Graphs of Polynomial Functions questions in NY Regents Algebra II Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Graphs of Polynomial Functions questions and exercises with answers

Showing questions 1–5 of 5.

How many times a factor appears in the factored form of a polynomial is called what?Read the answer and worked solution →A polynomial graph touches the x-axis at a zero and turns back. What does that show?Read the answer and worked solution →A polynomial function has degree 7. What is the largest number of turning points it can have?Read the answer and worked solution →For f(x) = (x + 2) cubed times (x - 5) squared times (x - 1), what is the degree?Read the answer and worked solution →Knock out the false claims about zerosRead the answer and worked solution →

Worked practice questions

How many times a factor appears in the factored form of a polynomial is called what?

  1. Its multiplicity
  2. Its coefficient
  3. Its leading term
  4. Its x-intercept
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Correct answer: A. Its multiplicity

1. Factor the polynomial and count how often one factor is repeated. 2. That count is called the multiplicity of the matching zero. 3. A factor written to the power 3 gives a zero of multiplicity 3. _Source: OpenStax Precalculus (CC BY 4.0), section 3.4 Graphs of Polynomial Functions_

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A polynomial graph touches the x-axis at a zero and turns back. What does that show?

  1. That zero has even multiplicity
  2. That zero has odd multiplicity
  3. That zero is not a real number
  4. That zero raises the degree by 1
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Correct answer: A. That zero has even multiplicity

1. Behaviour at an x-intercept is set by the power on the matching factor. 2. An even power makes the graph touch the axis and bounce back. 3. An odd power makes the graph pass through the axis. 4. So a touch and turn marks a zero of even multiplicity. _Source: OpenStax Precalculus (CC BY 4.0), section 3.4 Graphs of Polynomial Functions_

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A polynomial function has degree 7. What is the largest number of turning points it can have?

  1. Seven turning points
  2. Six turning points
  3. Eight turning points
  4. Five turning points
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Correct answer: B. Six turning points

1. A turning point is where the graph changes from rising to falling or from falling to rising. 2. The largest number of turning points is always one less than the degree. 3. With degree 7 that gives 7 minus 1, which is 6. 4. Reading the degree itself as the answer would give 7, which is the ceiling on x-intercepts instead. _Source: OpenStax Precalculus (CC BY 4.0), section 3.4 Graphs of Polynomial Functions_

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More Mathematics topics

Complex NumbersExponential and Logarithmic ModelsPower and Polynomial FunctionsRational FunctionsZeros of Polynomial FunctionsProperties of LogarithmsQuadratic FunctionsDividing Polynomials