Polynomial Graphs in Algebra

What does the end behavior of a polynomial function indicate?

Which of the following is a root 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)?

How many x-intercepts does the polynomial function have?

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?

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?

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.

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.