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Sketching Polynomials (CIE A Level Maths: Pure 1)
Revision Note
Sketching Polynomials
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
- 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
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