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

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Math Expert
Joined: 02 Sep 2009
Posts: 64951
On the graph above, when x = 1/2, y = 2; and when x = 1, y =  [#permalink]

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30 Jul 2012, 00:53
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On the graph above, when x = 1/2, y = 2; and when x = 1, y = 1. The graph is symmetric with respect to the vertical line at x = 2. According to the graph, when x = 3, y =

(A) -1
(B) -1/2
(C) 0
(D) 1/2
(E) 1

Practice Questions
Question: 7
Page: 153
Difficulty: 600

Attachment:

Graph.png [ 6.01 KiB | Viewed 42806 times ]

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On the graph above, when x = 1/2, y = 2; and when x = 1, y =  [#permalink]

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07 Oct 2017, 13:10
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Top Contributor
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Bunuel wrote:

On the graph above, when x = 1/2, y = 2; and when x = 1, y = 1. The graph is symmetric with respect to the vertical line at x = 2. According to the graph, when x = 3, y =

(A) -1
(B) -1/2
(C) 0
(D) 1/2
(E) 1

We're told that the graph of the parabola is symmetric with respect to the vertical line at x = 2
So, for example, notice that the point (0,3) lies on the parabola.
This point is 2 units to the LEFT of the line of symmetry.

This means that there's also a point that is 2 units to the RIGHT of the line of symmetry.
So, the coordinates of that point are (4,3)

Likewise, we're told that the point (1,1) lies on the parabola.
This point is 1 unit to the LEFT of the line of symmetry.

This means that there's also a point that is 1 unit to the RIGHT of the line of symmetry.
So, the coordinates of that point are (3,1)

Cheers,
Brent
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Math Expert
Joined: 02 Sep 2009
Posts: 64951
Re: On the graph above, when x = 1/2, y = 2; and when x = 1, y =  [#permalink]

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30 Jul 2012, 00:54
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8
SOLUTION

On the graph above, when x = 1/2, y = 2; and when x = 1, y = 1. The graph is symmetric with respect to the vertical line at x = 2. According to the graph, when x = 3, y =

(A) -1
(B) -1/2
(C) 0
(D) 1/2
(E) 1

Since the graph is symmetric with respect to line $$x = 2$$, then the value of $$y$$ when $$x = 3$$ will be the same as the value of $$y$$ when $$x = 1$$, so 1.

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Joined: 27 Jul 2012
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Re: On the graph above, when x = 1/2, y = 2; and when x = 1, y =  [#permalink]

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30 Jul 2012, 01:18
(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.
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Re: On the graph above, when x = 1/2, y = 2; and when x = 1, y =  [#permalink]

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02 Jan 2013, 06:18
1
Bunuel wrote:
Attachment:
Graph.png

On the graph above, when x = 1/2, y = 2; and when x = 1, y = 1. The graph is symmetric with respect to the vertical line at x = 2. According to the graph, when x = 3, y =

(A) -1
(B) -1/2
(C) 0
(D) 1/2
(E) 1

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.

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Joined: 07 Apr 2014
Posts: 95
Re: On the graph above, when x = 1/2, y = 2; and when x = 1, y =  [#permalink]

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09 Sep 2014, 10:12
1
Bunuel wrote:
Attachment:
Graph.png
On the graph above, when x = 1/2, y = 2; and when x = 1, y = 1. The graph is symmetric with respect to the vertical line at x = 2. According to the graph, when x = 3, y =

(A) -1
(B) -1/2
(C) 0
(D) 1/2
(E) 1

Practice Questions
Question: 7
Page: 153
Difficulty: 600

graph is symmetric with respect to the vertical line

so if x = 1, y = 1 & x=2 , y=0 then x=3 , y=1 ...
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Re: On the graph above, when x = 1/2, y = 2; and when x = 1, y =  [#permalink]

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19 May 2016, 09:24
6
Bunuel wrote:
Attachment:
Graph.png
On the graph above, when x = 1/2, y = 2; and when x = 1, y = 1. The graph is symmetric with respect to the vertical line at x = 2. According to the graph, when x = 3, y =

(A) -1
(B) -1/2
(C) 0
(D) 1/2
(E) 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.

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Re: On the graph above, when x = 1/2, y = 2; and when x = 1, y =  [#permalink]

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08 Apr 2020, 13:48
Bunuel wrote:

On the graph above, when x = 1/2, y = 2; and when x = 1, y = 1. The graph is symmetric with respect to the vertical line at x = 2. According to the graph, when x = 3, y =

(A) -1
(B) -1/2
(C) 0
(D) 1/2
(E) 1

Bunuel
What if x=4?
y would be 3?
Thanks__
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Re: On the graph above, when x = 1/2, y = 2; and when x = 1, y =  [#permalink]

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08 Apr 2020, 14:05
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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Math Expert
Joined: 02 Sep 2009
Posts: 64951
Re: On the graph above, when x = 1/2, y = 2; and when x = 1, y =  [#permalink]

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08 Apr 2020, 23:53
Bunuel wrote:

On the graph above, when x = 1/2, y = 2; and when x = 1, y = 1. The graph is symmetric with respect to the vertical line at x = 2. According to the graph, when x = 3, y =

(A) -1
(B) -1/2
(C) 0
(D) 1/2
(E) 1

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

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Yes.
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Re: On the graph above, when x = 1/2, y = 2; and when x = 1, y =   [#permalink] 08 Apr 2020, 23:53

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

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