Desmos SAT Cheat Sheet

Must-know moves for test day. Keep this open when you practice.

📈 Graphing Basics

Type any equation and press Enter — Desmos draws it instantly. No equals sign needed for y = f(x) form.
Graph multiple functions by adding a new line for each. Overlay them automatically to find intersections.
Restrict domain: y = 2x + 1 {0 <= x <= 5} — graphs only the segment you need.
Plot a specific point: type (3, 7) directly. Desmos marks it on the graph.
Click any intersection point to read the exact (x, y) coordinates.
Zoom to fit: press the home button (top right) or Ctrl+Shift+F.

📋 Using Tables

Click the + button and select "Table" to open a data table.
Enter x-values in the left column — Desmos auto-fills y-values from any linked equation.
Link a table to an equation: define y₁ = 2x₁ + 3 and the columns fill automatically.
Run linear regression: enter data pairs, then type y₁ ~ ax₁ + b on a new line.
Quadratic regression: y₁ ~ ax₁² + bx₁ + c
Exponential regression: y₁ ~ a·b^(x₁)

🎚️ Sliders

Type an undefined letter (a, b, k, h) in an equation — Desmos prompts you to create a slider.
For y = a(x-h)²+k, add sliders for a, h, k to drag the vertex in real time.
Set min/max/step in slider settings to match the problem's constraints.
Click the play ▶ button on a slider to animate — great for exponential growth/decay visualization.
Click "all" when prompted to create sliders for all undefined letters at once.

📉 Regression

Linear: y₁ ~ ax₁ + b — best-fit line through your data points.
Quadratic: y₁ ~ ax₁² + bx₁ + c — best-fit parabola.
Exponential: y₁ ~ a·b^(x₁) — best-fit exponential curve.
Desmos shows r² (0 to 1) — closer to 1 means the model fits better.
The fitted curve overlays your scatter plot automatically for visual confirmation.
Read the fitted equation parameters from the regression output panel.

⭕ Geometry

Draw a circle: (x-h)²+(y-k)²=r² — replace h, k, r with your values.
Verify a point is on a circle by plotting it — if it sits on the curve, it satisfies the equation.
Distance formula: sqrt((x₂-x₁)²+(y₂-y₁)²) — type it directly to evaluate.
Midpoint: ((x₁+x₂)/2, (y₁+y₂)/2) — type as a point to plot and verify.
Perpendicular lines have slopes that multiply to -1: if slope is m, perpendicular slope is -1/m.

⚡ Shortcuts & Hidden Features

✅ Check Your Work

Solved an equation? Graph both sides and click the intersection — coordinates confirm your answer.
System of equations? Graph both lines; the intersection is the solution.
Quadratic roots? Graph y = ax²+bx+c and click the x-intercepts.
Checking answer choices? Graph x = value for each option and see which hits the curve.
Inequality? Graph it — Desmos shades the correct region automatically.
Evaluate f(n)? Type f(3) and Desmos outputs the numeric result.

📝 Question Type → Desmos Move

Question Type	Recommended Desmos Move
Linear equation (solve for x)	Graph both sides as y = ... ; click intersection for x
System of equations	Graph both equations; click intersection point
Quadratic — find roots	Graph parabola; click x-intercepts
Quadratic — vertex form	Enter y = a(x-h)²+k with sliders for a, h, k; drag vertex
Inequality / region	Type inequality directly; shaded region is the solution set
Data analysis / scatter plot	Enter data in table; run regression (y₁ ~ ax₁ + b or quadratic)
Graph-matching question	Type each answer choice equation and match the shape
Circle / geometry	Type (x-h)²+(y-k)²=r²; plot given points to verify
Function evaluation f(n)	Define f(x), then type f(n) to get the numeric output

Practice with the official tools before test day