Final answer:
To find the value of a in the equation f(x) = -2x³ + ax² + 2, you can substitute the given value of x and solve for a. In this case, f(2) = 14 is given, so you can substitute 2 into the equation and solve for a to find the value of a is 7.
Step-by-step explanation:
To find the value of a, we are given that f(2) = 14. Substituting the value of x in the equation f(x) = -2x³ + ax² + 2, we have 14 = -2(2)³ + a(2)² + 2. Simplifying, we get 14 = -16 + 4a + 2. Combining like terms, we have 14 = 4a - 14. Moving the constants to the right side, we get 4a = 14 + 14. Simplifying, we find 4a = 28. Finally, dividing both sides by 4, we get a = 7.