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))

Suggested Video

 Finding the Minimum or Maximum of a Quadratic Function – mbrandl11

Finding the Minimum or Maximum of a Quadratic Function – SPHSLearningLab

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