Use the maximum,minimum, and zero options on your calculator.
Relative Maximum: (0.83,- 1.94) Relative Minimum: (6.16,- 3) and (2.88,- 12.17) Zeros: (- 0.60,0) and (3.71,0)
Practice makes perfect
To draw the graph using a calculator, we first press Y= and type the function in one of the available rows. Having written the function, we can push the GRAPH button to see an image of it.
For this function, we are unable to see the entire image because it does not fit in the standard viewing window. Let's resize the window by pushing WINDOW and changing the minimum and maximum of our axes. We want all of the relative minimums, maximums, and zeros to be clearly shown.
Relative Maximum and Minimum
This function has three extremes: two relative minimums and one relative maximum. To find the maximum, push 2nd, TRACE, and then choose the fourth option, maximum. Next, we need to choose a left bound and right bound for the maximum value. Finally, the calculator will ask for a guess of where the maximum might be.
We can do the same thing for the relative minimums. This time, however, we have to choose the third option, minimum.
The relative maximum is at (0.83,- 1.94), and the relative minimums are at (6.16,- 3) and (2.88,- 12.17).
Zeros
To find the zeros, we need to find the points at which the graph intersects the x-axis. This happens twice with this polynomial, so there are two zeros. To find a zero using the calculator, push 2nd, then TRACE, and choose the second option, zero. Once again, we need to choose bounds and make a guess for each zero.
