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A parabola has one x-intercept at (– 4, 0). If the vertex is at (2, 5

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Bunuel
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A parabola has one x-intercept at (– 4, 0). If the vertex is at (2, 5 [#permalink] New post   15 Mar 2015, 23:09
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A parabola has one x-intercept at (– 4, 0). If the vertex is at (2, 5), find the other x-intercept.

A. 5
B. 6
C. 7
D. 8
E. 9
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Bunuel
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Re: A parabola has one x-intercept at (– 4, 0). If the vertex is at (2, 5 [#permalink] New post   23 Mar 2015, 03:50
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Bunuel wrote:
A parabola has one x-intercept at (– 4, 0). If the vertex is at (2, 5), find the other x-intercept.

A. 5
B. 6
C. 7
D. 8
E. 9


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MAGOOSH OFFICIAL SOLUTION:

The line of symmetry of a parabola always passes through the vertex, so the equation of the line of symmetry is the vertical line x = 2. The two x-intercepts are symmetrical around this line. The point (– 4, 0) is six units to the left of the symmetry line, so the other should be six units to right, at (8, 0).
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awanish1r
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Re: A parabola has one x-intercept at (– 4, 0). If the vertex is at (2, 5 [#permalink] New post   16 Mar 2015, 10:05
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Parabola is symmetric about a line parallel to Y axis in this case. Therefore the X -coordinate distance of the other intercept is same from the vertex as the given intercept. The distance = 2-(-4)=6 , There the other coordinate is 2+6 = 8.
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Re: A parabola has one x-intercept at (– 4, 0). If the vertex is at (2, 5 [#permalink] New post   16 Mar 2015, 03:11
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Answer is D (8)

Parabola y= ax^2+bx+c

x intercept at (-4,0) then 16a-4b+c=0 <=> c =4b-16a (1)
Vertex (-b/2a;c- b^2/4a)=(2,5) then -b/2a=2 <=> b=- 4a (2)
(1)+(2)=> c=8b (3)
c- b^2/4a = 5 (4)
From (2)(3)(4) we have 8b- b^2/(-b)=5 <=> 9b= 5 then b =5/9 then c =40/9 and a = -5/36
the second intercept x we have -5/36 x^2+ 5/9x+40/9=0
<=> x^2-4x-32=0
Using back solving,we have x =8; 8^2-4*8-32=0
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Re: A parabola has one x-intercept at (– 4, 0). If the vertex is at (2, 5 [#permalink] New post   16 Mar 2015, 17:28
awanish1r wrote:
Parabola is symmetric about a line parallel to Y axis in this case. Therefore the X -coordinate distance of the other intercept is same from the vertex as the given intercept. The distance = 2-(-4)=6 , There the other coordinate is 2+6 = 8.

u are right. my way is silly :( too many years not study math sense is lost :(
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Re: A parabola has one x-intercept at (– 4, 0). If the vertex is at (2, 5 [#permalink] New post   14 Jul 2016, 06:22
Bunuel wrote:
A parabola has one x-intercept at (– 4, 0). If the vertex is at (2, 5), find the other x-intercept.

A. 5
B. 6
C. 7
D. 8
E. 9


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The coordinates makes it clear that we are dealing with a parabola like a "inverted U" or a "straight A"

One arm of the parabola is cutting the x axis at -4, the vortex is 2 the distance between the arm and vortex is 6 units .
THE OTHER ARM WILL BE A MIRROR IMAGE OF THE FIRST ARM... AN IMAGINARY VERTICAL LINE DRAWN THROUGH THE VORTEX WILL ACTS AS THE AXIS OF SYMMETRY.
The vortex is at x=2. Now the other arm will be 6 unit away from x=2
There fore the other arm will be at X=2+6 = 8
The x coordinate of the other arm will be 8

ANSWER IS D
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Re: A parabola has one x-intercept at (– 4, 0). If the vertex is at (2, 5 [#permalink] New post   26 Jul 2017, 23:16
The point of vertex is the midpoint for the parabola and hence we can consider the midpoint formula to calculate the other interscept. Am i correct in my concept . Kindly help.
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Re: A parabola has one x-intercept at (– 4, 0). If the vertex is at (2, 5 [#permalink] New post   27 Jul 2017, 00:01
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Bunuel wrote:
A parabola has one x-intercept at (– 4, 0). If the vertex is at (2, 5), find the other x-intercept.

A. 5
B. 6
C. 7
D. 8
E. 9


Kudos for a correct solution.


Vertex of the parabola is (2,5) . The x coordinate is 2.
So parabola is symmetrical about x =2

Parabola has x - intercept as (-4,0 ). Sodistance between x =2 and x-inctercept of arabola = 2-(-4) = 6
other x - intercept = (2+6,0) = (8.0)


Answer D
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Re: A parabola has one x-intercept at ( 4, 0). If the vertex is at (2, 5 [#permalink] New post   11 Mar 2024, 07:42
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Re: A parabola has one x-intercept at ( 4, 0). If the vertex is at (2, 5 [#permalink]
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