Tips: Plotting Functions and Analysis Tools

Plotting a Quadratic Function:

• Example: Height of a cannonball over time.

  • Enter function:

    • −2x²+20x+8

  • Adjust zoom settings for accurate visualization. (I suggest [ZOOM] -> 0)

Analysis Tools:

• Maximum Height:

  • Use "Maximum" tool.

  • After 5 seconds, cannonball reaches 58 meters.

• Time to Reach Ground:

  • Utilize "Zero" tool by pressing [2ND] + [TRACE] + 2

  • “Left bound?” -> Move “blinky” to left side of line from where it touches at zero

  • “Right bound?” -> move “blinky” to right side from where it touches at zero

  • “Guess?” -> place “blinky” on top of where it touches zero

  • Result: 10.38 (round up by three sig-figs) -> 10.4 

  • Interpretation: Cannonball touches ground at 10.4 seconds 

• Initial Height:

  • Plug in 0 for function; in most cases, getting an initial height can be found by isolating the constant alone.

  • In context: initial height is 8 meters.

• Time to Reach Specific Height:

  • Plot horizontal line (e.g., at 40 meters).

  • Use "Intersection" tool.

  • Cannonball reaches 40 meters in 2 seconds.

Tips: Numeric Solver

• Numeric Solver (N Solve) is a valuable function on TI-84 for solving equations quickly and accurately.

• It's particularly essential for topics like exponential, logarithmic, quadratic, and cubic functions.

• Accessing Numeric Solver:

  • Access the function by navigating to [MATH] > [C:Numeric Solver] 

• Entering Equation:

  • Input the equation directly into the calculator, ensuring correct syntax and using 'X' as the variable.

• Specifying Bounds:

  • Specify appropriate bounds to narrow down the search range for the solution.

  • Bounds should be close to the expected solution for faster convergence.

• Initiating Calculation:

  • Press [GRAPH] button when ready to start “guessing”

  • Input any value for X (as long as it fits in context to problem)

  • Result will be displayed in the same area you input a value in

• Viewing Result:

  • The calculator displays the approximate solution once the calculation is complete.

  • REMEMBER TO USE THREE SIG-FIGS

• Considerations:

  • Numeric Solver provides the left-hand solution for equations with multiple solutions.

  • For equations with multiple solutions or complex functions, consider using other analysis tools like plotting functions and intersection analysis.