Mathematics (AS)·Equations, expressions, identities and inequalities · NSSCAS 1.1.1
Completing the square & the vertex
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In this lesson you will learn to complete the square for any quadratic, first when the number in front of x squared is one, and then when it is not. You will discover how the completed-square form hands you the turning point of the graph for free. Finally, you will sketch a full, labelled parabola showing the vertex, the y-intercept and the line of symmetry. It is one of the most rewarded skills in the whole AS course.
What you'll learn in this lesson
By the end you should be able to (NSSCAS Mathematics (AS) 1.1.1):
- Complete the square for a quadratic function ax² + bx + c, both when a = 1 and when a ≠ 1
- Use the completed-square form y = a(x + p)² + q to determine the turning point (vertex) of the graph
- Sketch the graph of a quadratic from its completed-square form, showing the vertex, orientation, y-intercept and line of symmetry
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