Complete the input-output table for the function f(x)=(x−2)^2+3

Question

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Drag and drop each number. Match the function with the correct answer.
(1 point)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.

1 Response area

2 Response area
3 Response area

4 Response area

Answer 1

To complete the input-output table for the function \( f(x) = (x - 2)^2 + 3 \), we will calculate the output (f(x)) for various input values (x).

Let's choose some input values (for example, x = 0, 1, 2, 3, 4) and calculate the corresponding outputs.

1. For \( x = 0 \): \[ f(0) = (0 - 2)^2 + 3 = (2)^2 + 3 = 4 + 3 = 7 \]

2. For \( x = 1 \): \[ f(1) = (1 - 2)^2 + 3 = (-1)^2 + 3 = 1 + 3 = 4 \]

3. For \( x = 2 \): \[ f(2) = (2 - 2)^2 + 3 = (0)^2 + 3 = 0 + 3 = 3 \]

4. For \( x = 3 \): \[ f(3) = (3 - 2)^2 + 3 = (1)^2 + 3 = 1 + 3 = 4 \]

5. For \( x = 4 \): \[ f(4) = (4 - 2)^2 + 3 = (2)^2 + 3 = 4 + 3 = 7 \]

Now we can summarize the results in an input-output table format:

| Input (x) | Output (f(x)) | |-----------|---------------| | 0 | 7 | | 1 | 4 | | 2 | 3 | | 3 | 4 | | 4 | 7 |

You can now drag and drop the outputs 7, 4, 3, 4, and 7 into the corresponding response areas in your table based on the inputs you've selected.