The coordinates of three points are labeled on the parabola in the xy-

Question

https://gmatclub.com/forum/download/file.php?id=64232 The coordinates of three points are labeled on the parabola in the xy-plane above. Which of the following could be the equation of the parabola? (A) y = (x – 4)(x + 2) (B) y = (x – 2)(x + 4) (C) y = (x–2)^2 – 4 (D) y = (x – 4)(x + 2) – 8 (E) y = (2 – x)(x + 4) 1.png

GMATinsight · Answer

Simply Substitute the points in Options and check
e.g. For (0, -8) to be on Graph at x=0l, y should be -8
Options A and B satisfy but Options C, D and E can be eliminated

Now, for (2, 0) to be on graph, at x=2, y should be come 0
Option A doesn't satisfy and only Option B satisfies hence

Answer: Option B

Crytiocanalyst · Answer

(2,0) is only satisfied by B and D

(-8,0) is only satisfied by B

Therefore IMO B

MathRevolution · Answer

As per the co-ordinates (x + 4) ( x - 2)

Answer B

Sr1994 · Answer

First of all, we don't know the vertex. 
From the given graph, we have  2 X intercepts -4 & 2 .

If we don't know the vertex, we can use the equation  Y=a(X-P)(X-Q)  ---- (1), where P and Q are X intercepts.

Now, we have to find out  a .
Plugging in the values of P and Q into Eq:1, we get,  Y=a(X+4)(X-2)  ---- (2)

Now, we have a 3rd point (0,-8). We can use this point to find the value of  a .
Plugging in (0,-8) in Eq:2, we get,
-8 = a(0+4)(0-2)
-8 = a(4*(-2))
-8 = -8a
 a = 1

Now, if we substitute the value of a in Eq:2, we get,  Y = (X+4)(X-2)

Answer B

bumpbot · Answer

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The coordinates of three points are labeled on the parabola in the xy-

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The coordinates of three points are labeled on the parabola in the xy-

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