Final answer:
To find the equation of the parabola, substitute the given points and x-intercepts into the general equation and solve the system of equations.
Step-by-step explanation:
The equation of a parabola that passes through the point (5, 35) and has x-intercepts of -5 and 12 can be represented in the form y = ax^2 + bx + c.
To find the equation, we need to substitute the coordinates of the point and the x-intercepts into the equation and solve the resulting system of equations.
When we substitute (5, 35) into the equation, we get 35 = 25a + 5b + c.
When we substitute (-5, 0), we get 0 = 25a - 5b + c, and when we substitute (12, 0), we get 0 = 144a + 12b + c.
Solving this system of equations will give us the values of a, b, and c, and we can then substitute them back into the equation y = ax^2 + bx + c to get the final equation of the parabola.