14. Find the equation of the parabola $y=a x^{2}+b x+c$ that passes through the points $(1,2),(-1,-4)$, and $(2,8)$.

Step 1 ：We are given the points (1,2), (-1,-4), and (2,8) and we need to find the equation of the parabola $y=a x^{2}+b x+c$ that passes through these points.

Step 2 ：We can substitute the x and y values from the given points into the equation to get three equations: For point (1,2): $2 = a(1)^2 + b(1) + c$, For point (-1,-4): $-4 = a(-1)^2 + b(-1) + c$, For point (2,8): $8 = a(2)^2 + b(2) + c$

Step 3 ：We then solve this system of equations to find the values of a, b, and c.

Step 4 ：The solution to the system of equations gives us the values of a, b, and c as 1, 3, and -2 respectively.

Step 5 ：Therefore, the equation of the parabola that passes through the points (1,2), (-1,-4), and (2,8) is $y = 1x^2 + 3x - 2$.

Step 6 ：Final Answer: The equation of the parabola is \(\boxed{y = x^{2} + 3x - 2}\).