What vertical parabola contains the points (1,-3), (2,1), and (3,11). answer by writing its cartesian (x, y) equation in simplest form.

So hmmm the idea being, you have 3 points, and thus a system of equations of 3 variables

so hmm say for example for a quadratic equation, which is what a parabolic graph is, the template is more or less => y = ax² + bx + c

now, we dunno what a,b, and c, are, but we know three points, (1,-3), (2,1), and (3,11), so let us plug those fellows in



so, that's our system of equations of three variables, and now, we'd use say hmm elimination, to say hmmm see what "a" is, so, let's eliminate the variable "c" then, by using equations 1) and 2) there

let's multiply equation 1) by -1 then



now, let us do the same, and eliminate "c" again, from equations 1) and 3)
and again, let's multiply by -1 in the equation 1)



so.. now, let's use those "resultant" equations of two variables, and say hmmm eliminate "b", by simply multiplying 4 = 3a + b  times  -2





thus