Final answer:
The correct equation for the parabola is not listed in the provided options, but the process involves using the factored form and the point (2, -18) to find the correct equation. The closest answer is option A, which suggests there may be an error in the question or options.
Step-by-step explanation:
The equation for a parabola that passes through the point (2, -18) with x-intercepts at (-1,0) and (4,0) can be determined by using the factored form of a quadratic equation, y = a(x - r)(x - s), where r and s are the roots of the parabola.
In this case, the roots are x = -1 and x = 4. Therefore, the equation starts as y = a(x + 1)(x - 4).
Now we need to find the value of 'a' that will make the parabola pass through the point (2, -18). Substituting the point into the equation gives us -18 = a(2 + 1)(2 - 4) which simplifies to -18 = a(3)(-2), so a = 3. Thus, our equation now becomes y = 3(x + 1)(x - 4).
To find the standard form of the equation, we expand the factored form: y = 3(x^2 - 4x + x - 4), which simplifies to y = 3(x^2 - 3x - 4). Multiplying each term by 3, we get the equation y = 3x^2 - 9x - 12. Comparing this with the given options, none of them is correct but option A is the closest to the correct form. It seems there might be an error in the question or in the provided options.