Resources / Functions

📈 Graph and analyse a function

Type the function and see its graph with the axis crossings, the vertex if it is a parabola and the slope if it is a line, each with its steps.

Function

y =

Understood: 2x + 3 · x^2 − 4x + 3 · x² · (x − 1)(x + 2) · 0.5x · 1/x · sqrt(x)

Examples:
y = x² − 4x + 3
xy−3−2−1123456510152025Y-axis crossing (0, 3)(0, 3)X-axis crossing (1, 0)(1, 0)X-axis crossing (3, 0)(3, 0)Vertex (2, −1)(2, −1)

Points

  • Y-axis crossing:(0, 3)
  • X-axis crossing:(1, 0)
  • X-axis crossing:(3, 0)
  • Vertex:(2, −1)

Axis of symmetry

x = 2

Opens

upwards (a > 0)

Where it crosses the Y axis

  1. On the Y axis, x is 0. Substitute:
  2. y = f(0) = 3 → (0, 3)

Where it crosses the X axis

  1. On the X axis, y is 0. Solve:
  2. x² − 4x + 3 = 0
  3. Quadratic formula with a = 1, b = −4, c = 3: x = (−b ± √(b² − 4ac)) / 2a
  4. Discriminant: b² − 4ac = (−4)² − 4·1·3 = 4
  5. x = (4 ± √4) / 2 → x₁ = 1 and x₂ = 3

Vertex

  1. xᵥ = −b / 2a = 4 / 2 = 2
  2. yᵥ = f(2) = −1
  3. a = 1 is positive: the parabola opens upwards and the vertex is its lowest point (minimum).

Practise functions

📈 Function Hunt📝 Functions exam📝 Lines exam🖨️ More resources
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