How to Manipulate Graphs in iOS 18 Math Notes

Apple’s iOS 18 introduces a dynamic graphing feature within Math Notes that transforms handwritten equations into interactive visual plots. This article covers how touch gestures allow users to explore and adjust these graphs, detailing specific controls for panning, zooming, resizing, and dynamically modifying plotted variables directly on the screen.

Generating the Graph

To create a graph, write an equation with one or two variables (such as \(y = 2x + 3\)) using your finger or an Apple Pencil in the Notes or Calculator app. Math Notes detects the expression and suggests the option to insert a graph. Selecting this option embeds an interactive coordinate grid directly into the document adjacent to the handwritten text.

Panning Across the Coordinate Plane

Once the graph appears, navigating different sections of the axes requires basic touch navigation:

  • Single-Finger Drag: Touch and drag anywhere inside the coordinate grid to shift the viewing window. This moves the origin and allows you to trace functions further along the x- or y-axis.
  • Auto-Centering: Double-tapping the graph resets the viewport to the default origin point \((0,0)\).

Pinching to Zoom

Adjusting the scale of the axes uses standard iOS multi-touch gestures:

  • Pinch In and Out: Place two fingers on the graph area and pinch together to zoom out, revealing a broader range of the function. Spread two fingers apart to zoom in for a detailed view of local minima, maxima, intercepts, or intersections.
  • Aspect Ratio Maintenance: Math Notes scales both axes proportionally during standard zoom gestures to preserve the geometric accuracy of the plotted function.

Real-Time Scrubbing and Variable Manipulation

The most powerful touch manipulation connects the graph to the handwritten equation itself:

  • Interactive Number Scrubbing: Tap a handwritten coefficient or constant in the equation to reveal an adjustment slider.
  • Touch-and-Drag Values: Dragging your finger horizontally along the slider or over the number alters the value in real time. The plotted curve shifts, rotates, or morphs instantaneously on the graph to reflect the numeric change.

Overlaying Multiple Functions

You can plot multiple functions on the same grid to locate points of intersection. Write a secondary equation near the existing graph, tap the equation, and select the option to add it to the existing plot. Once added, panning and zooming gestures navigate both functions simultaneously without unlinking their shared scale.

Resizing and Repositioning the Graph

  • Resizing the Window: Tap the graph card to display bounding handles at the corners and edges. Drag these handles outward or inward to expand or shrink the graph's dimensions within the note.
  • Repositioning: Long-press the graph container until it lifts from the background, then drag it to a new location within the note layout to align it with relevant notes or calculations.