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The coordinates of three points are labeled on the parabola in the xy- 22 Oct 2021, 08:15
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70% (01:39) correct 30% (01:50) wrong based on 172 sessions

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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) \(y = (2 – x)(x + 4)\)

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The coordinates of three points are labeled on the parabola in the xy- 22 Oct 2021, 21:16
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Bunuel

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) \(y = (2 – x)(x + 4)\)

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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
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The coordinates of three points are labeled on the parabola in the xy- 22 Oct 2021, 22:53
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Bunuel

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) \(y = (2 – x)(x + 4)\)

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

(-8,0) is only satisfied by B

Therefore IMO B
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The coordinates of three points are labeled on the parabola in the xy- 22 Oct 2021, 23:52
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As per the co-ordinates (x + 4) ( x - 2)

Answer B
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The coordinates of three points are labeled on the parabola in the xy- 10 Feb 2022, 00:46
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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
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The coordinates of three points are labeled on the parabola in the xy- 03 Mar 2025, 10:20
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