Step-by-Step: Plotting a Function
- Find the y-intercept by setting x = 0.
- Find the x-intercept(s) by setting y = 0 and solving.
- Plot a few additional points by substituting sample x-values.
- Connect the points smoothly, respecting the function's known shape (line, parabola, curve).
Worked Example
Graph y = x² − 4x + 3.
Y-intercept: y = 3 at x=0. Roots: factor to (x−1)(x−3) = 0, so x=1 and x=3.
Vertex sits halfway between the roots at x=2: y = 4−8+3 = −1. The parabola opens upward with a minimum at (2, −1).
Frequently Asked Questions
How many points do I really need to plot?
For a straight line, just 2. For a parabola, the vertex plus 2-3 surrounding points is usually enough to see the shape clearly.
How do I graph functions other than parabolas?
The same core process applies: find intercepts, identify key points, and understand the general shape (line, cubic, exponential, etc.) before connecting points smoothly.
