On the graph above, when x = 1/2, y = 2; and when x = 1, y =

(E) 1

its symmetric with respect to x=2.
when x=1, 1 unit to the left of x(2), y is 1.
when x=3, 1 unit to the right of x(2), y should again be 1 as it is symmetric.

Half of the entire graph is a mirror image of the other side. The center coordinate is (2,0) according to the graph. Thus, y when x=1 and y when x-3 are equal.

Answer: E

graph is symmetric with respect to the vertical line

so if x = 1, y = 1 & x=2 , y=0 then x=3 , y=1 ...

We are given that the graph is SYMMETRIC along the vertical line x = 2. We are also given that when x = 1, y = 1. We are asked to determine the value of y when x is 3. Keep in mind that when x = 1, it is ONE UNIT away from the line x = 2, and when x = 3, it is also ONE UNIT away from the line x = 2.

Since the y-coordinate is 1, when x is 1, the y-coordinate is ALSO 1 when x is 3. Again, this is because the graph is symmetric with the line x = 2.

Another way to look at this problem is to see that the point (1,1) is actually being reflected over the line x = 2.

We see that the point (1,1) is exactly 1 unit from the line x = 2. In fact the point (2,1) is on the line x = 2 which is exactly 1 unit from (1,1). However, (1,1) is exactly 1 unit on the LEFT of (2,1), so by symmetry, the point that is exactly 1 unit on the RIGHT of (2,1) is (3,1). Thus the y-coordinate is 1.


Answer E.

Bunuel
What if x=4?
y would be 3?
Thanks__

Y would be 1 as it is symmetrical around 2 so y at X=1 equal to y at x=3

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Yes.

BrentGMATPrepNow

I was just curious and tried to come up with the equation of the parabola but couldn't figure it out. Isn't (2, 0) the vertex of the parabola?

It LOOKS like (2, 0) is the vertex, but it isn't.

According to the given information, we know that the graph is symmetric with respect to the vertical line at x = 2. This means that if we reflect any point on the graph across the line x = 2, we will obtain another point on the graph.

Given that when x = 1/2, y = 2, we can observe that this point is located 1.5 units to the left of the line x = 2. Therefore, if we reflect this point across the line x = 2, the corresponding y-coordinate will be the same, but the x-coordinate will be 1.5 units to the right of the line x = 2.

So, the reflected point will have an x-coordinate of 2 + 1.5 = 3.5.

However, we are asked to find the value of y when x = 3, not x = 3.5. Since the graph is symmetric with respect to the line x = 2, the y-coordinate will also be symmetric. Thus, the value of y when x = 3 will be the same as the value of y when x = 3.5.

Given that when x = 1, y = 1, we can conclude that when x = 3, y will also be (E) 1.