Quadratic Equation General Formular
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Quadratic Equation General Formular
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Chart_curve Quadratic Equation General Formular

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Any quadratic function can be written in the standard form f(x) = a(x - h) 2 + k

where  h  and  k  are given in terms of coefficients  a   b  and  c  

Let us start with the 
quadratic function in general form and complete the square to rewrite it in standard form. 
  • Given function f(x) 
    f(x) = ax 2 + bx + c
  • factor coefficient a out of the terms in x 2 and x 

    f(x) = a ( x 2 + (b / a) x ) + c
  • add and subtract (b / 2a) 2 inside the parentheses 
    f(x) = a ( x 2 + (b/a) x + (b/2a) 2 - (b/2a) 2 ) + c
  • Note that 
    x 2 + (b/a) x + (b/2a) 2
  • can be written as 
    (x + (b/2a)) 2
  • We now write f as follows 
    f(x) = a ( x + (b / 2a) ) 2 - a(b / 2a) 2 + c
  • which can be written as 
    f(x) = a ( x + (b / 2a) ) 2 - (b 2 / 4a) + c
  • This is the standard form of a quadratic function with h = - b / 2a k = c - b 2 / 4a

When you graph a quadratic function , the graph will either have a maximum or a minimum point called the vertex. The  x  and  y  coordinates of the vertex are given by  h  and  k  respectively. 
04-04-2016 10:17 AM
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