What is the equation, in standard form, of a parabola that models the values in the table? x~ -2 , 0 , 4 f(x)~ 1 , 5 , -59

The equation can be obtained using microsoft excel, using manual substitution or using the statistics function of the calculator (I recommend Casio Fx 991-ES)

the equation that you will get from this method is initially 

f(x) = y = -3x^2 - 4x + 5

converting this equation to the standard form, we obtain

Standard form: (x-h)^2 = -4a(y-k)

by completing the square

we can obtain

(x + 2/3)^2 = (-1/3)(y - 19/3)

you can recheck your answers by substituing the values