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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.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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