I am learning basically how to graph quadratic equations. I dont really
understand how to find the coordinates of the vertex. I also don't understand
how to write an equation of the axis of symmetry. Can you please help me?
 
For the equation y or f(x) = a(x-h)2 + k

The vertex is this point:  (h, k)

The equation of the axis of symmetry is  this:  x = h

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For the equation y or f(x) = ax2 + bx + c

The vertex is this point:  ( -b/(2a), c - b2/(4a)  )

The equation of the axis of symmetry is  this:  x = -b/(2a)

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Example 1:  y = -4(x+4)2-3

Compare to  y =  a(x-h)2+k

-h = +4, so h = -4
 k = -3.

The vertex is this point:  (h, k) = (-4,-3)

The equation of the axis of symmetry is  this:  x = h, or x = -4

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Example 1: Find the vertex of f(x) = 2x2 - 12x + 19

                    Compare to f(x) = ax2 + bx + c

                                a = 2; b = -12; c = 19

The vertex is this point:  ( -b/(2a), c - b2/(4a)  ) =

( -(-12)/(2·2), 19 - (-12)2/(4·2)  )

      ( 12/4, 19 - 144/8  )  =

          ( 3, 19 - 18) =

               (3,1)

The equation of the axis of symmetry is  this: x = -b/(2a) 

                                                x = -(-12)/(2·2)

                                                x = 3 

Edwin
AnlytcPhil@aol.com