Desmos Calculator Mastery • Lesson 2 of 7
Graph Plotting
Type an equation, read its key features, and let the picture replace the algebra.
To plot, type y = followed by the rule. Use ^ for powers (x^2), * for multiply, and sqrt( ) for a square root. Press Enter and the curve appears; type a new row to add another graph in a new colour.
- Type
y = x^2 - 5x + 6into a row.A U-shaped parabola is drawn. - Turn on
key pointsunder the graph.The calculator marks the roots at x = 2 and x = 3 (where it crosses the x-axis). - Read the picture instead of factoring.The crossings ARE the solutions of x^2 - 5x + 6 = 0.
On a graph, the x-intercepts are the zeros (solutions), the y-intercept is the constant term, and the lowest or highest point of a parabola is its vertex. If a curve runs off the screen, zoom out so you can see the whole shape before you read anything.
Try it livePlot a parabola and find its roots
- The parabola
y = x^2 - 5x + 6is already loaded. - Tick key points below the graph to mark the roots.
- Try changing it to
y = x^2 - 4x + 3and watch the roots move.
Formula Reference Sheet
This chapter
Fast moves
| Solve f(x)=0 | graph y=f(x); turn on key points |
|---|---|
| Solve an equation | graph both sides; read where they meet |
| Evaluate | use the Scientific tab |
Digital SAT reference
Area & Circumference
| Circle area | A = πr² |
|---|---|
| Circle circumference | C = 2πr |
| Rectangle | A = ℓw |
| Triangle | A = ½ b h |
Volume
| Rectangular box | V = ℓwh |
|---|---|
| Cylinder | V = πr²h |
| Sphere | V = 4⁄3 πr³ |
| Cone | V = 1⁄3 πr²h |
| Pyramid | V = 1⁄3 ℓwh |
Right triangles
| Pythagorean theorem | a² + b² = c² |
|---|---|
| 30°–60°–90° | sides x : x√3 : 2x |
| 45°–45°–90° | sides s : s : s√2 |
Constants
| Degrees in a circle | 360° |
|---|---|
| Radians in a circle | 2π |
| Angles of a triangle | sum = 180° |
🖩 Graphing Calculator