Question

Question 7

Let f (x) = -2x³ + ax² +2. You are told that f (2) = 14, what is the value of a ?
a=9
a=8
a=7
a=6

Answer 1

a = 7

Explanation:

Substitute x for 2 and f(x) for 14

14 = -2(2³) + a(2²) + 2

14 = -16 + 4a + 2

14 = -14 + 4a

14 + 14 = 4a

28 = 4a

4a = 28

Divide both sides by 4

4a/4 = 28/4

a = 7

Alternative:

Since from the question, you're already told that f(2) = 14, you just have to find the number that can be multiplied by 2 with a resultant of 14; that number is 7. To confirm, substitute a for 7 in the equation.