Write the quadratic function in vertex form: f(x) = 4x2 + 2x -5A)f(x) = 4(x + 14)2 - 214B)f(x) = 4(x + 116)2 - 214C)f(x) = 4(x + 14)2 - 194D)f(x) = 4(x + 116)2 - 194

Please use " ^ " to denote exponentiation:  f(x) = 4x^2 + 2x -5.  To find the vertex form of this equation, complete the square:

f(x) = 4x^2 + 2x                                           - 5
      = 4(x^2 + (2/4)x)                                         - 5
      =  4(x^2 + (1/2)x )                                  -5
      = 4(x^2 + (1/2)x + 1/16  ) - 4/16 - 5
      = 4(x+1/4) - 21/4    <= in vertex form

Here h= -1/4 and k = -21/4.  The vertex is at (-1/4, -21/4)