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IB Applications & Interpretations Topic 3 - Functions (SL and HL)

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.

IB Applications & Interpretations Topic 3 - Functions (SL and HL)

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.

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