A-LEVEL•Mathematics•Quadratics•1.1 Completing the Square & Vertex Form

Why it matters

Rewrite ax^2 + bx + c as a(x + p)^2 + q to find the vertex, line of symmetry and greatest or least value.

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Why it matters

The form $ax^2 + bx + c$ is good for finding the $y$ -intercept, but it hides the most useful point on the graph: the vertex. Rewriting the quadratic as

a(x+p)^2 + q

shows the vertex immediately, because a square is never negative.

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1.2 The Discriminant & Nature of Roots