Sketching Polynomials (AQA AS Maths): Revision Note
Did this video help you?
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

Unlock more revision notes. It's free!
By signing up you agree to our Terms and Privacy Policy.
Already have an account? Log in
Did this page help you?