Question

ind a quadratic function that models the data. Round numerical values to the nearest whole number.

f(x) =
x2 +
x +

Answer 1

To find a quadratic function that models the data, we need at least 3 data points.

Let's say the data points are (1, 3), (2, 8), and (3, 15).

Using these data points to form a system of equations:

1. 3 = a(1)^2 + b(1) + c
2. 8 = a(2)^2 + b(2) + c
3. 15 = a(3)^2 + b(3) + c

Simplify the equations:

1. 3 = a + b + c
2. 8 = 4a + 2b + c
3. 15 = 9a + 3b + c

Now, solve the system of equations to find the values of a, b, and c:

From the first equation:
c = 3 - a - b

Substitute c in the second equation:
8 = 4a + 2b + 3 - a - b
8 = 3a + b + 3
5 = 3a + b

Substitute c in the third equation:
15 = 9a + 3b + 3 - a - b
15 = 8a + 2b
7 = 4a + b

Now we have a system of equations:
5 = 3a + b
7 = 4a + b

Solve this system of equations to find:
a = 2
b = -1

Now, substitute a and b back into the first equation to find c:
3 - 2 + 1 = 2

Therefore, the quadratic function that models the data is:

f(x) = 2x^2 - x + 2