Answer: f(x) = -1/2x^2 + 40x
Step-by-step explanation: Let the blanks be a, b, and c according to the standard f(x) = ax^2 + bx + c. To find c, plug (0, 0) into the equation: 0 = 0x^2 + 0x + c
This simplifies to 0 = c
To find b, we can pick any two x and f(x) values to be subtracted. I will use 4, 152 and 6, 222.
4, 152 plugged into the equation is 152 = 16a + 4b (Multiply 4 by itself for a)
Divide the entire equation by 4 to simplify: 38 = 4a + b
6, 222 is 222 = 36a + 6b (Multiply 6 by itself for a)
Divide the entire equation by 6 to simplify: 37 = 6a + b
We can now subtract the two equations (the b cancels out): 1 = -2a
Divide both sides by -2 to get -1/2 = a
We can now solve for b by plugging -1/2 into the equation 37 = 6a + b
37 = 6(-1/2) + b
37 = -3 + b
Add 3 on both sides: 40 = b
This means that the function that models the situation is f(x) = -1/2x^2 + 40x + 0 (the zero does not need to be included for c)
