Final answer:
The equation of the quadratic function with roots -3 and 4 that passes through the point (5, 40) is y = 5x^2 - 5x - 60.
Step-by-step explanation:
To determine the equation of a quadratic function with roots -3 and 4 that passes through the point (5, 40), we can use the factored form of a quadratic equation ax2 + bx + c = 0. Since the roots are -3 and 4, the factored form of the equation is a(x + 3)(x - 4) = 0. To find the value of 'a', we use the given point (5, 40).
Plugging the point into the equation, we get: a(5 + 3)(5 - 4) = 40. This simplifies to 8a = 40, so a = 5. Now, we know the equation is y = 5(x + 3)(x - 4).
After expanding, the quadratic equation is: y = 5x2 - 5x - 60. This is the standard form of the quadratic equation we were looking for.