# Completing the square - Applications

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

Completing the Square : Tutorial 1 : ExamSolutions
This is a short tutorial on completing the square.
Example:
Express x2 + 6x - 1 in the form (x + p)2 + q stating the value of p and q.

Completing the Square - Applications (1 of 3)
Completing the Square can be applied to showing that a quadratic expression is positive or negative for all real values of x.
Examples:
Show that x2 - 6x + 10 > 0.
Show that -7 + 5x - x2 < 0.

Completing the Square - Applications (2 of 3) | Sketching Quadratic Graphs (Part 1)
Completing the Square can be used to help sketch quadratic graphs, locating maximum and minimum points and lines of symmetry. In part 1 of this series, we will look at sketching quadratic graphs that have a positive x squared coefficient.
Examples:
y = x2 - 8x + 6
y = 2x2 + 8x + 1.

Completing the Square - Applications (3 of 3) | Sketching Quadratic Graphs (Part 2)
In part 2 of this series, we will look at sketching quadratic graphs that have a negative x squared coefficient.

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