Introduction
Finding maximum and minimum values comes up often in algebra, precalculus, calculus, physics, economics, and engineering. Students usually need to find the highest or lowest point on a graph to solve optimization problems, analyze functions, or finish assignments.
The TI-84 calculator has built-in tools that let you find local maximums and minimums right from the graph.
This guide will show you how to find maximum and minimum values on a TI-84 calculator. You’ll see the button steps, examples, common mistakes, and helpful tips.
When Should You Find Maximum and Minimum Values?
You may need to find maximums and minimums when:
- Solving optimization problems.
- Finding the highest or lowest point on a graph.
- Analyzing quadratic functions.
- Studying polynomial functions.
- Working with business or economics applications.
- Solving calculus problems involving turning points.
For example, if a company wants to get the most profit or spend the least, finding maximum and minimum values can help them find the best answer.
What Are Maximum and Minimum Values?
A maximum value is the highest point a function reaches in a certain range.
A minimum value is the lowest point a function reaches in a certain range.
For example:
The graph has:
- A minimum point at x = 2
- A minimum value of y = -1
Since the parabola opens upward, it has a minimum point instead of a maximum.
Step-by-Step Instructions
Finding a Maximum Value
Step 1: Open the Y= Editor
Press:
Y=
Step 2: Enter the Function
Example:
-X² + 4X + 5
Step 3: Graph the Function
Press:
GRAPH
You should now see the graph on your screen.
Step 4: Open the CALC Menu
Press:
2ND
TRACE
This will open the CALC menu.
Step 5: Select Maximum
Choose:
4:Maximum
Press:
ENTER
Step 6: Choose the Left Bound
Move the cursor to the left side of the maximum point.
Press:
ENTER
Step 7: Choose the Right Bound
Move the cursor to the right side of the maximum point.
Press:
ENTER
Step 8: Guess Near the Maximum
Move the cursor near the peak.
Press:
ENTER
The calculator will show you the coordinates of the maximum point.
Result
For:
[
y=-x^2+4x+5
]
y=-x^2+4x+5
]
The calculator gives you:
x = 2
y = 9
So, the maximum value is:
9
Finding a Minimum Value
Step 1: Enter the Function
Example:
X² – 4X + 3
Step 2: Press GRAPH
GRAPH
Step 3: Open the CALC Menu
Press:
2ND
TRACE
Step 4: Select Minimum
Choose:
3:Minimum
Press:
ENTER
Step 5: Select Left Bound
Move the cursor left of the minimum point.
Press:
ENTER
Step 6: Select Right Bound
Move the cursor right of the minimum point.
Press:
ENTER
Step 7: Guess Near the Minimum
Move the cursor near the bottom point.
Press:
ENTER
Result
The calculator shows:
x = 2
y = -1
So, the minimum value is:
-1
Worked Example 1
Problem
Find the maximum value of:
[
y=-x^2+6x-2
]
y=-x^2+6x-2
]
Enter the Function
Y=
-X²+6X-2
Press:
GRAPH
Use Maximum Feature
Press:
2ND
TRACE
4
ENTER
Select:
- Left Bound
- Right Bound
- Guess
Calculator Result
x = 3
y = 7
Answer
The maximum value is:
7
Worked Example 2
Problem
Find the minimum value of:
[
y=x^2-8x+10
]
y=x^2-8x+10
]
Use Minimum Feature
Press:
2ND
TRACE
3
ENTER
Select:
- Left Bound
- Right Bound
- Guess
Calculator Result
x = 4
y = -6
Answer
The minimum value is:
-6
How to Find the Maximum and Minimum of a Quadratic Quickly
For quadratic functions:
[
y=ax^2+bx+c
]
y=ax^2+bx+c
]
The vertex occurs at:
[
x=\frac{-b}{2a}
]
x=\frac{-b}{2a}
]
The TI-84 graphing method finds this value for you automatically.
For example:
The vertex is:
(2,-1)
which is also the minimum point.
Common Errors
1. Wrong Graph Window
Sometimes the maximum or minimum point is outside the visible graph window.
Solution:
Press:
ZOOM
6:ZStandard
2. Incorrect Left and Right Bounds
The left bound must be to the left of the turning point.
The right bound must be to the right of the turning point.
If not, the calculator may return an error.
3. Selecting the Wrong Feature
Students often choose:
3:Minimum
when they actually need:
4:Maximum
Be certain to double-check before you press ENTER.
4. Entering the Function Incorrectly
Example:
Incorrect:
-X^2+4
When the intended function was:
-(X^2)+4X
Check your equation before you graph it.
5. Graph Not Visible
If no graph appears:
Check:
- Window settings
- Graph style
- Function entry
Using:
ZOOM
6:ZStandard
This usually fixes the problem.
Tips for Faster Results
- Use ZStandard before searching for extrema.
- Zoom in near turning points for higher accuracy.
- Verify results by checking the graph visually.
- Store important functions in Y1.
- Use TRACE to inspect nearby values.
Frequently Asked Questions
What is the difference between a maximum and minimum?
A maximum is the highest point on a graph.
A minimum is the lowest point on a graph.
Can the TI-84 find local maximums and minimums?
Yes.
The Maximum and Minimum functions in the CALC menu are specifically designed for this purpose.
Why does the calculator ask for bounds?
Bounds help the calculator determine which turning point you want to analyze.
This is especially important for graphs with multiple peaks and valleys.
Can I find maximum and minimum values without graphing?
For simple quadratics, you can use the vertex formula.
For more complicated functions, graphing is usually easier.
Why am I getting an error message?
Common causes include:
- Incorrect bounds
- Graph not visible
- Function entered incorrectly
- No maximum or minimum exists within the selected interval
Conclusion
The TI-84 calculator makes it easy to find maximum and minimum values using the CALC menu. Once you graph the function, just pick the Maximum or Minimum option, set the bounds, and let the calculator find the turning point.
For most algebra and calculus problems, the process is:
- Enter the function.
- Graph it.
- Open the CALC menu.
- Choose Maximum or Minimum.
- Select bounds.
- Read the coordinates.
Learning how to use this feature can save you time, help you be more accurate, and make solving optimization and graphing problems easier.
Dr. Vivienne Blackwell
Dr. Vivienne Blackwell is a mathematics and educational technology specialist focused on TI-84 calculator online tools, graphing calculator simulations, algebra, calculus, and statistics problem-solving systems. She creates structured and optimised guides that explain how to use TI-84 emulators and online calculator platforms for accurate equation solving, function graphing, and exam-focused mathematical analysis.