Question

use the graph of the function to complete the table.

Explanation:

Since the table is not fully shown (only the header "input" and "output" is visible), we assume typical input values (x - values) to find output (y - values) from the graph. Let's take common x - values like \(x = 1\), \(x = 2\), \(x = 4\), \(x = 6\), \(x = 7\).

Step 1: For \(x = 1\)

Locate \(x = 1\) on the x - axis. Move up to the graph, then left to the y - axis. The y - value (output) is \(0\) (since the graph starts at \(x = 1\) with \(y = 0\)).

Step 2: For \(x = 2\)

Locate \(x = 2\) on the x - axis. Move up to the graph, then left to the y - axis. The y - value is \(4\) (from the graph's curve at \(x = 2\)).

Step 3: For \(x = 4\)

Locate \(x = 4\) on the x - axis. Move up to the graph (the vertex), then left to the y - axis. The y - value is \(7\) (the peak of the parabola at \(x = 4\)).

Step 4: For \(x = 6\)

Locate \(x = 6\) on the x - axis. Move up to the graph, then left to the y - axis. The y - value is \(4\) (symmetric to \(x = 2\) since the parabola is symmetric about \(x = 4\)).

Step 5: For \(x = 7\)

Locate \(x = 7\) on the x - axis. Move up to the graph, then left to the y - axis. The y - value is \(0\) (symmetric to \(x = 1\) about \(x = 4\)).

Answer:

input (\(x\))	output (\(y\))
2	4
4	7
6	4
7	0

(Note: If the intended input values are different, the output will change accordingly. This is a general approach based on the visible graph and typical function table completion.)