Theory of Intelligence
11TH•Mathematics•Theory Of Quadratic Functions•Exercise 3.1

Key ideas

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Key ideas

Vertex form:

f(x)=a(x−h)2+k f(x)=a(x-h)^2+k
  • If a>0a>0, then f(x)≥kf(x)\ge k and the minimum value is kk.
  • If a<0a<0, then f(x)≤kf(x)\le k and the maximum value is kk.

Completing the square:

x2+bx=(x+b2)2−(b2)2 x^2+bx=\left(x+\frac{b}{2}\right)^2-\left(\frac{b}{2}\right)^2

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