Question

Identify a quadratic function that fits the points (0, 3), (1, 2), and (3, 12).

0 f(x) = -2x² - x + 3
0 f(x) = 2x² + x - 3
0 f(x) = -2x² + x + 3
0 f(x) = 2x² + x + 3

Answer 1

The quadratic function that fits the points (0, 3), (1, 2), and (3, 12) can be computed by solving the system of equations derived from plugging these points into the general form of a quadratic equation. However, the solution found does not exactly match any of the options provided, suggesting a possible typo in the question. The nearest option to the correct equation is f(x) = 2x² + x + 3 with an understanding that the coefficient for x might be incorrect.

Step-by-step explanation:

To identify a quadratic function that fits the points (0, 3), (1, 2), and (3, 12), we can plug these points into the general form of a quadratic function f(x) = ax² + bx + c and solve for the coefficients a, b, and c.

For the point (0, 3), we get:

• f(0) = a(0)² + b(0) + c = 3

This immediately tells us that c = 3.

For the point (1, 2), we get:

• f(1) = a(1)² + b(1) + 3 = 2
• a + b = -1 (after subtracting 3 from both sides)

For the point (3, 12), we get:

• f(3) = a(3)² + b(3) + 3 = 12
• 9a + 3b = 9 (after subtracting 3 from both sides)

Now we have a system of equations:

1. a + b = -1
2. 9a + 3b = 9

Solving this system, we find:

• a = 2
• b = -3

Therefore, the quadratic function that fits the points given is f(x) = 2x² - 3x + 3. However, this option is not listed above, which suggests there may be a typo in the question. If this is indeed a typo and the correct function was intended to be among the options, f(x) = 2x² + x + 3 is the nearest to our solution but has a positive instead of a negative coefficient for x. Hence, due to the possible error in the options provided, we should verify the question and the available choices before selecting the final answer.