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

**Plotting a Quadratic Function:**

**Example: Height of a cannonball over time.**Enter function:

−2x

^{2}+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.

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.

**Plotting a Quadratic Function:**

**Example: Height of a cannonball over time.**Enter function:

−2x

^{2}+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.

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.