ti 84 plus ce color graphing calculator

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Quadratic Equation Solver

Standard Form: ax² + bx + c = 0

Discriminant (Δ):
Root 1 (x₁):
Root 2 (x₂):

How to Use the Quadratic Solver

The TI-84 Plus CE Color Graphing Calculator is a powerful tool for algebra students. One of its most frequently used functions is solving quadratic equations. While the calculator has a built-in "Solver" function, understanding the manual calculation using the Quadratic Formula is essential for your exams.

Understanding the Inputs

To find the x-intercepts (roots) of a parabola, you need the equation in Standard Form: ax² + bx + c = 0.

  • a: The coefficient of the squared term. It determines if the parabola opens up or down.
  • b: The coefficient of the linear term.
  • c: The constant term where the graph crosses the y-axis.

Checking Your Work on the TI-84 Plus CE

After using the calculator above, you can verify the results by graphing the equation on your TI-84 Plus CE:

  1. Press the [Y=] key.
  2. Enter your equation next to Y1.
  3. Press [GRAPH].
  4. Press [2ND] then [TRACE] (Calc) and select "2: zero".
  5. Move the cursor to the left of the intercept, press Enter, then right of the intercept, and press Enter twice to find the exact root.

Why the Discriminant Matters

The calculator above displays the Discriminant (Δ = b² – 4ac). This value tells you how many solutions to expect:

  • Δ > 0: Two distinct real solutions (the graph crosses the x-axis twice).
  • Δ = 0: One real solution (the vertex touches the x-axis).
  • Δ < 0: Two complex solutions (the graph does not touch the x-axis).

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