Sketching the graph of a polynomial

• Remember 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!)

How do I sketch a graph of 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

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