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