Use the standard form #y = ax^2+bx+c# and the 3 points to write 3 equations with, a, b, and c as the variables and then solve for the variables.
Because the question specifies a function, we must discard the form that is not a function:
and use only the form:
Using the point #(0,3)# , we substitute 0 for x and 3 for y into equation [1] and the solve for c:
Substitute 3 for c into equation [1]:
Using the point #(1,-4)# we substitute 1 for x and -4 for y into equation [1.1] to obtain an equation that contains "a" and "b" as variables:
We do the same thing using the point #(2,-9)#
Write equations [2] and [3] together as a system of equations:
Multiply both sides of equation [2] by -2 and add the results to equation [3]:
#4a-2a +2b-2b = -12+14#
This makes the terms containing "b" become 0:
Substitute 1 for "a" into equation [2] and then solve for "b":
Substitute 1 for "a" and -8 for "b" into equation [1.1]:
Here is a graph of the 3 points and equation [1.2]: