Polynomial Graphs in Algebra
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Polynomial Graphs in Algebra

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@CongratulatoryHeliotrope2700

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Questions and Answers

What does the end behavior of a polynomial function indicate?

  • The number of x-intercepts of the function.
  • The direction the graph rises or falls at the ends. (correct)
  • The maximum value of the function.
  • How the graph behaves as it approaches the x-axis.

    • Which of the following is a root of the polynomial function y = (x – 2)(x – 1)(x + 3)?

  • -1
  • -3 (correct)
  • 2 (correct)
  • 0

    • What is the y-intercept of the polynomial function y = (x – 2)(x – 1)(x + 3)?

  • -6
  • 0
  • 6 (correct)
  • 1

    • How many x-intercepts does the polynomial function have?

    <p>3</p> Signup and view all the answers

    What is the effect of a polynomial factor having an even degree?

    <p>The graph does not cross the x-axis at that root.</p> Signup and view all the answers

    When graphing the polynomial function, what point would be classified as the maximum?

    <p>(-1, 12)</p> Signup and view all the answers

    Which of the following represents an incorrect step when graphing a polynomial?

    <p>Ignoring the x-intercepts.</p> Signup and view all the answers

    What is the y value at the x-intercept of the polynomial function?

    <p>0</p> Signup and view all the answers

    Study Notes

    Polynomial Graphs

    • The behavior of a polynomial graph at the left and right sides is called end behavior.
    • End Behavior refers to how the graph rises or falls to the left and right.
    • X-Intercepts are points where the graph crosses the x-axis.
    • Y-Intercepts are points where the graph crosses the y-axis.
    • Turning Points are points where the graph changes from increasing to decreasing or vice versa.
    • The number of turning points in a polynomial graph is less than or equal to one less than the degree of the polynomial.

    Graph Example

    • Equation: y = (x - 2)(x - 1)(x + 3)

    Steps to Graph a Polynomial Function

    • Step 1: Identify the roots (zeros) of the polynomial function.
      • Set each factor equal to zero and solve for x.
      • This gives us the x-intercepts.
    • Step 2: Find the y-intercept.
      • Substitute x = 0 into the polynomial equation and solve for y.
      • This gives us the y-intercept.
    • Step 3: Create a table of values.
      • Choose several x-values, including those found in steps 1 and 2.
      • Substitute each x-value into the polynomial equation and solve for y.
      • This gives you coordinates to plot.
    • Step 4: Plot the points from Step 3 on the graph.
    • Step 5: Sketch a smooth curve through the plotted points.
      • Use the end behavior and turning points to guide the shape of the curve.

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    Related Documents

    Polynomial Functions: X and Y Intercepts - Graphs

    Description

    This quiz covers key concepts related to polynomial graphs, including end behavior, x-intercepts, y-intercepts, and turning points. You will learn how to identify these features and apply them to graphing polynomial equations. Test your understanding of polynomial function behavior and graphing techniques.

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