Final answer:
The equation of the parabola is y = 3x^2 - 22x + 7.
Step-by-step explanation:
The equation of a parabola with x-intercepts (-1,0) and (4,0) which passes through the point (1,-12) can be found by using the form of a quadratic equation. Let's assume the equation is of the form y = ax^2 + bx + c. Substituting the x and y values of the given point, we get -12 = a(1)^2 + b(1) + c which can be rearranged to get a + b + c = -12. Further, substituting the x-intercepts (-1,0) and (4,0), we get -a + b - c = 0 and 16a + 4b + c = 0 respectively.
Solving these three equations simultaneously, we find that a = 3, b = -22, and c = 7.
Therefore, the equation of the parabola is y = 3x^2 - 22x + 7.