How to Solve Quadratic Equations on TI 84 Calculator

Quadratic equations often feel more difficult than linear equations because they involve curves instead of straight lines. Many students struggle to solve quadratic equations on a TI 84 calculator tool, even when they understand the math concept. Common problems include entering the equation incorrectly, not knowing how to find solutions on the graph, or misinterpreting calculator results.

These issues usually happen because quadratic equations behave differently than linear ones, and students are unsure how the calculator represents solutions. In this guide, you will learn how to solve quadratic equations on a TI 84 calculator step by step, using clear methods that students and teachers can trust.

What You Need Before Starting

Before solving quadratic equations, make sure the calculator is ready.

TI 84 Calculator Compatibility

This guide applies to:

TI 84
TI 84 Plus
TI 84 Plus CE

All these models handle quadratic equations in the same way.

Required Calculator Settings

Before starting:

Calculator must be in Function mode
Angle mode should be set correctly
Old equations should be cleared if not needed

Correct settings help ensure accurate graph results.

Math Prerequisites

You should understand:

Quadratic equations in the form ax² + bx + c = 0
Basic graph interpretation
Meaning of x-values and y-values

No advanced algebra techniques are required.

How to Use the TI-84 Calculator

The TI 84 calculator solves quadratic equations by displaying them as graphs. When a quadratic equation is entered correctly, the calculator shows a curved graph called a parabola. The solutions to the equation appear where the graph crosses the x-axis.

Understanding how to switch between equation entry, graph mode, and result interpretation helps students solve quadratic equations confidently and accurately.

Step-by-Step Solution Using TI 84

We will solve the following example:

x² − 5x + 6 = 0

Step 1: Rewrite the Equation

Ensure the equation is set equal to zero
The equation is already in correct form

This format is required for solving using graphs.

Step 2: Enter the Equation

Press Y=
Enter: X^2 - 5X + 6 next to Y₁
Press ENTER

The equation is now stored.

Step 3: Graph the Equation

Press GRAPH
A curved graph (parabola) should appear

If the graph is not visible, reset the graph window.

Step 4: Find the Solutions (Zeros)

Press 2nd → TRACE
Select 2:Zero
Move the cursor to the left of the first x-intercept and press ENTER
Move to the right of the intercept and press ENTER
Press ENTER again to confirm

The calculator displays the x-value solution.

Step 5: Find the Second Solution

Repeat the zero-finding steps for the other intercept

Quadratic equations usually have two solutions.

Step 6: Interpret the Results

The x-values where the graph crosses the x-axis are the solutions
These values satisfy the original equation

Understanding this helps connect graphs with algebra.

Common Mistakes and How to Fix Them

Mistake 1: Equation Entered Incorrectly

Why it happens:
Students forget the squared term or use the wrong key.

Fix:
Use the X² key or exponent key correctly.

Mistake 2: Missing One Solution

Why it happens:
Students find only one x-intercept.

Fix:
Check both sides of the parabola for intercepts.

Mistake 3: Graph Not Visible

Why it happens:
The graph window is not set correctly.

Fix:
Reset the window to standard view.

Using the Online TI-84 Tool

The same steps can be practiced using the TI 84 Calculator Tool available on this website. The online tool allows students to enter quadratic equations, view parabolic graphs, and find solutions accurately without needing a physical calculator.