Question 816049: The axis of symmetry of a parabola is the line x=4.
The x-intercepts are 10 and -2.
Suppose that the point (12,4) is on the graph;what other point must also be on the graph?
I keep getting the point (4,4) would be on the graph but it is wrong. What am I doing wrong and what point is on the graph? Thanks for any help.
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! the axis of symmetry of the parabola is the line x = 4
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this means that you can fold a graph of the parabola along the above line and the two halves of the graph will overlap perfectly.
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if the point p1 (12, 4) is on the parabola then another point p2 symmetrical to it must also be on the parabola.
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reflect p1 (12, 4) about the axis of symmetry x = 4
the other point p2 is at distance dx from the axis of symmetry:
dx = 12 - 4 = 8
but on the opposite side of the axis of symmetry:
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Answer:
the other point (p2) is:
x = 4 - dx
x = 4 - 8
x = -4
y = 4 (from the y-coordinate of p1)
(-4, 4)
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