Examining Graphs of  Polynomial Equations of Higher Degree Topic Index | Algebra2/Trig Index | Regents Exam Prep Center

Examples:

1.  Given the graph at the right,                    ,    estimate the zeroes of the function. (Remember, the zeroes are the locations where the graph crosses the x-axis.) This graph crosses the x-axis between -1 and 0, at 1, and between 2 and 3. By observation, one estimated answer may be:                      -0.75, 1, and 2.75 This question could also have asked you to approximate the solutions to the equation .  The answers would be the same.

Now, let's use the zero option (2nd Calc) on the graphing calculator to get a more accurate estimate of the zeroes and check out our observed answers. .     Looks like our observed answers were very close to being correct.

 

2.  Use the graph at the right to estimate the solutions of the equation . Look carefully at this question.  This equation was NOT set equal to zero and then graphed.  Instead, the expression on each side of the equal sign was graphed separately.  You are not looking to find where the blue graph crosses the x-axis.  You are looking to find where the blue graph and the red graph intersect. By observation, one estimated answer may be:                         -2.5, 0, and 1.5  This problem could also be solved by setting the original equation equal to zero.

Now, let's use the intersect option (2nd Calc) on the graphing calculator to get a more accurate estimate of the zeroes and check out our observed answers. .     Again, our observed answers were very close to being correct. (Remember that entries such as x = 2.684E-15 are really 0. By scientific notation, 2.684E-15 equals 0.000000000000002684.)