When you press
you see a list of options as shown below.
Options 1 and 2 are discussed in the evaluating and zeros lesson
. This lesson will focus on options 3:minimum and 4:maximum. Let’s start by using the minimum feature.
Enter the equation
into your calculator and graph
it in a
The minimum of this graph
is at the vertex
of the parabola. The value of the vertex
can be computed using a formula (vertex lesson
) or by using the calculator.
From the graph
and choose option 3. You have asked the calculator to find a minimum point
on this graph. To perform this operation, you must tell the calculator where to look for this minimum value.
The screen you see is asking for the Left Bound of the region (interval) you would want the calculator to look in.
If your cursor is not already somewhere to the left of the vertex
use the left arrow key
to move the cursor to the left of the minimum point.
The calculator is now asking for the right boundary of the search. Use the right arrow key
to place the cursor to the right of the minimum value.
When the calculator asks for Guess?
You simply press
and the answer will be on the bottom of the screen.
The screen shows the minimum value at (1, -5). This is the vertex
of the parabola. Notice that the calculator was not exact on the screen shown above. You may have ended up with an x – value of 0.999987 or something else really close to 1. This is a calculator limitation and you must learn to recognize when the calculator has not been able to be exact.
If a parabola
opens down, the vertex
is the maximum point
on the graph
and can be found by using option 4 (maximum) from the CALCULATE menu. Graph
to see that the vertex
of this parabola
is a maximum.
The process for finding a maximum is identical to finding a minimum. You will need to set a left bound and a right bound for the calculator to search. Make sure you can find the maximum of this parabola
at (2.5, -1.75).
Again notice that in my computations, the x-value did not turn
out to be exactly 2.5. You may have had a similar problem, but you should report your answer as x = 2.5.
Use the maximum or minimum feature to find the vertex
of each parabola
below. Make sure you can get the answers that are given.
1. 2. 3.
- maximum at (0, -2). Be careful if you get something in scientific notation for the x-value. This is the calculator way for giving zero as an answer.
It is possible to use the minimum or maximum feature to find a low or high point
or a function
that is not a parabola. The graph
Notice there is a place where the graph
peaks and begins to go back down. (It looks to be around x = -3) and a place where the graph
bottoms out and begins to go back up (it looks to be between x = -1 and x = 0).
The process for finding these localized minimum and maximum values is the same as it was for a quadratic. Make sure you can find a maximum at (-3.12, 4.06) and a minimum at (-0.21, -8.21)
Notice you can also find the zeros of this function. You should be able to find the zeros of the function
at x = -4, x = -2 and x = 1.
If you need help using the zero computation, go to the Using the CALCULATE menu-Part I lesson
. To learn more about zeros, click here
Use the maximum or minimum feature to find the maximum and minimum values of the functions below.
- local maximum at (-1.3, 0.3) and a local minimum at (1.3, -8.3)
- local minimum at (-1.67, -7.48) and a local maximum at (1, 2) a