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)