Final answer:
The equation of a parabola with x-intercepts at (1/5, 0) and (-3, 0) and passes through the point (0, 3) is y = 2x^2 - 5x + 3.
Step-by-step explanation:
To find the equation of a parabola with x-intercepts at (1/5, 0) and (-3, 0) and passes through the point (0, 3), we need to use the general form of a parabolic equation, which is y = ax^2 + bx + c. Plug in the x-intercepts into the equation to get two equations: 0 = a(1/5)^2 + b(1/5) + c and 0 = a(-3)^2 + b(-3) + c. Plug in the point (0,3) to get the equation 3 = a(0)^2 + b(0) + c. We now have a system of three equations with three unknowns (a, b, and c) that can be solved using algebra or matrices. After solving, we find that the equation of the parabola is y = 2x^2 - 5x + 3, so the correct answer is (c) y = 2x^2 - 5x + 3.