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More Lessons for A Level Maths

Math Worksheets

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)

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 = x^{2} - 2x + 7

y = x^{2} + 2x - 3

y = 1 - 6x + x^{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.

More Lessons for A Level Maths

Math Worksheets

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

Sketching Quadratic Graphs by Completing the Square (part 1)

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 = x

y = x

y = 1 - 6x + x

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.

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