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
