Maximum and Minimum Value of Quadratic Functions - The Alternative Method

The Alternative Method

f(x)=a x 2 +bx+c f(x)=a( x 2 + b a x+ c a ) f(x)=a[ x 2 + b a x+ ( b 2a ) 2 ( b 2a ) 2 + c a ] f(x)=a[ ( x+ b 2a ) 2 ( b 2a ) 2 + c a ] f(x) is minimum/maximum when ( x+ b 2a )=0 or x= b 2a 
  1. From the calculation above, we find that f(x) is minimum or maximum when \(x = - \frac{b}{{2a}}\) and we can find the minimum/maximum value of f(x) by substituting \(x = - \frac{b}{{2a}}\) into the equation.
  2. Therefore, the minimum/maximum point of the quadratic function is \(\left( { - \frac{b}{{2a}},f( - \frac{b}{{2a}})} \right)\)

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