Consider the function f(x) = x(x-4).

Question

If the point (2 + c, y) is on the graph of f(x), the following point will also be on the graph of f(x)
A) (c -2,y)
B) (2 - c,y)

Answer 1

To determine the x-coordinate of the second point, we substitute the given value of y into the equation:

y = (2 + c)(2 + c - 4)
y = (2 + c)(c - 2)
Plug in c - 2 for x:
y = (c - 2)(c - 2 - 4)
y = (c - 2)(c - 6)

Now, to find the x-coordinate of the second point, we substitute c - 2 into the equation f(x) = x(x - 4):

x = c - 2
x - 4 = (c - 2) - 4
x - 4 = c - 6

So, the point (c - 2, y) will also be on the graph of f(x).
Therefore, the answer is A) (c - 2, y).

Answer 2

y = x(x-4) = (x-2)^2 - 4
so the graph is symmetric about the line x=2.
So if x=2+c is on the graph, so is x = 2-c
The answer is B

Answer 3

You are correct. The graph of the function is symmetric about the line x = 2. So, if the point (2 + c, y) is on the graph of f(x), then the point (2 - c, y) will also be on the graph.
Therefore, the answer is B) (2 - c, y).