Theory of Intelligence
A-LEVEL•Mathematics•Quadratics•Exercise 1.1

Key idea: completing the square

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Key idea: completing the square

Take out the coefficient of x2x^2 first, then halve the coefficient of xx inside the bracket:

ax2+bx=a[(x+b2a)2−b24a2]a x^2 + bx = a\left[\left(x + \tfrac{b}{2a}\right)^2 - \tfrac{b^2}{4a^2}\right]

The vertex of a(x+p)2+qa(x+p)^2 + q is (−p, q)(-p,\ q). See Lesson 1.1.

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