Question

A parabola contains the following points.(-5,8),(2,-3),(3,1) which of the following systems of equations could be solved in order to find the equation that corresponds to this parabola?

Answer 1

Generic parabola equation:

y = a*x^2 + b*x + c

We have three points of the parabola:

(-5,8), (2,-3), (3,1)

For the point (-5, 8): x = -5, y = 8

8 = 25*a - 5*b + c

Point (2,-3): x = 2, y = -3

-3 = 4*a + 2*b + c

Point (3, 1): x = 3, y = 1

1 = 9*a + 3*b + c

Our system of equations:

8 = 25*a - 5*b + c

-3 = 4*a + 2*b + c

1 = 9*a + 3*b + c

The last option is the correct answer