Final answer:
To find the function y = ax^2 + bx + c that passes through the given points, substitute the coordinates into the equation and solve the resulting system of equations. The function is y = 2x^2 - 2x.
Step-by-step explanation:
To find the function y = ax^2 + bx + c that passes through the points (1,4), (-2,40), and (2,12), we can substitute the coordinates of each point into the equation and solve the resulting system of equations.
By substituting the coordinates (1,4), (-2,40), and (2,12) into the equation, we get the following system of equations:
4 = a(1)^2 + b(1) + c
40 = a(-2)^2 + b(-2) + c
12 = a(2)^2 + b(2) + c
Solving this system of equations will give us the values for a, b, and c, and we can then write the equation in the form y = ax^2 + bx + c.
Using the method of substitution or elimination, we can find that a = 2, b = -2, and c = 0. Therefore, the function y = 2x^2 - 2x.