Question 199338: Hello!
Find a function whose graph is a parabola with vertex (5, -7) and that passes through the point (4, 1).
thanks for your help!
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! There are actually two parabolas that meet this criteria, a "y" parabola, and an "x" parabola
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the standard form for a "y" parabola is ,,,, ( y-k) = a (x-h)^2, where (h,k) is the vertex
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substituting our data,,,, vertex at (5, -7) and (4,1),,,,, ( y-(-7) ) = a (x-5)^2
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@ ( 4,1),,,, (1) +7 =a ( 4-5)^2,,,,8=a(1),,,, a=8
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"y" parabola is y+7 = 8(x-5)^2,,,or y= 8(x-5)^2 -7
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to check substitute in both given points,,,ok
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The standard form for an "x" parabola is,,,,,(x-h) =a ( y-k)^2
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or (x-5) = a (y+7)^2,,,,,and @ (4,1),,,,, (4-5) = a (1+7)^2,,,,a= -1/64
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or (x-5) = -1/64 (y+7)^2,,,,,or x= -1/64 (y+7) ^2 +5
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to check substitute in both sets of points,,,,,,ok
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