Question 598215: find an equation in the form y-k=a(x-h)^2 for the parabola with axis of symmetry x=-2and contains the points(0,1) and (2,-5)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! find an equation in the form y-k=a(x-h)^2 for the parabola with axis of symmetry x=-2and contains the points(0,1) and (2,-5)
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standard form of equation for a parabola:
y=A(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex, A is a coefficient which affect the slope or steepness of the curve
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axis of symmetry, x=-2, means the x-coordinate of the vertex=-2
Using coordinates of given points,(0,1) and (2,-5), to set up two equations with unknowns A and k:
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1=A(0+2)^2+k
-5=A(2+2)^2+k
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1=4A+k
-5=16A+k
subtract to eliminate k
6=-12A
A=-1/2
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4=16A+4k
-5=16A+k
subtract to eliminate A
9=3k
k=3
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Equation:
y=-1/2(x+2)^2+3
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