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Question 526102: how do i solve this problem idk where to begin or how to do it?
Find an equation of a parabola that contains the points (1,4)(2,7) and (4,25)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! how do i solve this problem idk where to begin or how to do it?
Find an equation of a parabola that contains the points (1,4)(2,7) and (4,25)
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Standard equation for a parabola: y=A(x-h)^2+k
There are 3 variables you must solve: A, h, and k, and you have 3 known points on the curve.
The approach, then, is to set up 3 equations with the 3 known points.
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(1) 4=A(1-h)^2+k
(2) 7=A(2-h)^2+k
(3) 25=A(4-h)^2+k
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(1) 4=A(1-h)^2+k
4=A(1-2h+h^2)+k
(4) 4=A-2Ah+Ah^2+k
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(2) 7=A(2-h)^2+k
7=A(4-4h+h^2)+k
(5) 7=4A-4Ah+Ah^2+k
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(4) 4=A-2Ah+Ah^2+k
(5) 7=4A-4Ah+Ah^2+k
subtract eq (5) fm eq(4)
(6) -3=-3A+2Ah
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(3) 25=A(4-h)^2+k
25=A(16-8h+h^2)+k
(7) 25=16A-8Ah+Ah^2+k
(5) 7=4A-4Ah+Ah^2+k
subtract eq (5) fm eq(7)
(7) 18=12A-4Ah
(6) -3=-3A+2Ah
multiply eq(6) by 2
(8) -6=-6A+4Ah
Add eq(8) and eq(7)
(9) 12=6A
A=2
(6) -3=-3A+2Ah
-3=-6+4h
4h=3
h=3/4
(4) 4=A-2Ah+Ah^2+k
4=2-3+1.125+k
k=3.875
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Ans:
A=2, h=.75, k=3.875
Equation of parabola:
y=2(x-.75)^2+3.875
see graph below as a visual check on the answers:
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comment: This is quite a marathon. Hope you can follow it ok. The answers I got check with my computer graphing program.
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