**Form** | **Feature revealed** a x2+bx+c, a 0 | Intercept (0,c) a(x-p)(x-q) | Zeros p,q a(x-h)2+k | Vertex (h,k); symmetry x=h Example x2-6x+5=(x-1)(x-5)=(x-3)2-4. Zeros are 1,5, the vertex is (3,-4), and the minimum value is -4. Solve by factorising, completing the square or x= -b+-sqrt(b2-4ac)2a. For x2-6x+5=4, completing the square gives (x-3)2=8, hence x=3+-2 2.

\(x^2-6x+5=(x-1)(x-5)=(x-3)^2-4\). Zeros are \(1,5\), the vertex is \((3,-4)\), and the minimum value is \(-4\).

Solve by factorising, completing the square or \(x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\). For \(x^2-6x+5=4\), completing the square gives \((x-3)^2=8\), hence \(x=3\pm2\sqrt2\).

Quadratic Functions, Equations and Inequalities

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Quadratic forms and equations

Quadratic forms and equations