Podcast
Questions and Answers
What does the end behavior of a polynomial function indicate?
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)?
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)?
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?
How many x-intercepts does the polynomial function have?
What is the effect of a polynomial factor having an even degree?
What is the effect of a polynomial factor having an even degree?
When graphing the polynomial function, what point would be classified as the maximum?
When graphing the polynomial function, what point would be classified as the maximum?
Which of the following represents an incorrect step when graphing a polynomial?
Which of the following represents an incorrect step when graphing a polynomial?
What is the y value at the x-intercept of the polynomial function?
What is the y value at the x-intercept of the polynomial function?
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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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