Graphing Calculator
One Calculator, Six Function Families
Most functions students and engineers actually work with fall into a handful of shapes — a straight line, a curve that bends once, one that bends twice, exponential growth or decay, a repeating wave, or a slowing logarithmic climb. Rather than solving each by hand, this calculator evaluates any of the six at a chosen x-value once you supply the relevant coefficients.
The Formulas
Linear: y = mx + b
Quadratic: y = ax² + bx + c
Cubic: y = ax³ + bx² + cx + d
Exponential: y = a × b^x
Sine: y = a × sin(bx + c)
Logarithmic: y = a × ln(x) + b
Quadratic: y = ax² + bx + c
Cubic: y = ax³ + bx² + cx + d
Exponential: y = a × b^x
Sine: y = a × sin(bx + c)
Logarithmic: y = a × ln(x) + b
Worked Example
For the quadratic y = x² − 3x + 2, evaluated at x = 5:
| Step | Calculation | Result |
|---|---|---|
| x² term | 1 × 5² | 25 |
| x term | −3 × 5 | −15 |
| y | 25 − 15 + 2 | 12 |
Where This Matters
- Checking a function at a point — verifying a homework answer, a physics prediction, or a spreadsheet formula's output.
- Modeling growth and decay — the exponential mode covers population growth, radioactive decay, and compound interest curves.
- Signal and wave analysis — the sine mode evaluates any point along an oscillating signal with a given amplitude, frequency, and phase.
How to Use This Calculator
- Choose the function type: Linear, Quadratic, Cubic, Exponential, Sine, or Logarithmic.
- Enter the coefficients for that function (for example, Coefficient a, Coefficient b, and so on).
- Enter the x value where you want the function evaluated.
- Select Calculate to get the resulting y value.
Related Calculations
Working with a straight line specifically? The Line Equation Calculator derives m and b directly from two points.