Sketching Polynomials (Edexcel IAL Maths)

Spec point — 1.11

Sketching polynomials

How do I sketch the graph of a polynomial?

• A polynomial is any finite function with non-negative indices, that could mean a quadratic, cubic, quartic or higher power

• When asked to sketch a polynomial you'll need to think about the following

  • y-axis intercept
  • x-axis intercepts (roots)
  • turning points (maximum and/or minimum)
  • a smooth curve(this takes practice!)

What steps should I take when sketching a polynomial?

STEP 1 Find the y-axis intercept by setting x = 0

STEP 2 Find the x-axis intercepts (roots) by setting y = 0

STEP 3 Consider the shape and “start”/”end” of the graph

eg. a positive cubic graph starts in third quadrant (“bottom left”) and “ends” in first quadrant (“top right”)

STEP 4 Consider where any turning points should go

STEP 5 Draw with a smooth curve

• Coordinates of turning points can be found using differentiation
• Except with a point of inflection, repeated roots indicate the graph touches the x-axis

Worked Example