Completing the square and graph transformations

Examples, solutions, videos, activities and worksheets that are suitable for A Level Maths.

How to sketch quadratic graphs by completing the square?

Sketching Quadratic Graphs by Completing the Square (part 1)

Sketching Quadratic Graphs by Completing the Square (part 2)

C1 - Completing the Square (Harder) and curve sketching
When the coefficient of x-squared is not 1 - these are harder.
Sketching curves using the completed square form: Vertex and equation of line of symmetry.

Using Completing the Square to sketch graphs
Manipulate a quadratic equation (the second half covers negative quadratics) to get the completed square form and then use this as a short cut to sketching the curve and finding the coordinates of the minimum / maximum.
Example:
By completing the square, find the maximum or minimum value of y and the value of x for which this occurs. State whether your value of y is a maximum or minimum in each case.
y = x² - 2x + 7
y = x² + 2x - 3
y = 1 - 6x + x²

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