Question 572994: Find an equation in standard form of the parabola passing through the following points.
(0,-4),(1,1),(2,8)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find an equation in standard form of the parabola passing through the following points.
(0,-4),(1,1),(2,8)
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Standard form of equation for a parabola: y=A(x-h)^2+k, (h,k) being the (x,y) coordinates of the vertex.
..
Solve for A, h and k with the following 3 equations using 3 given points:
1)-4=A(0-h)^2+k
2)1=A(1-h)^2+k
3)8=A(2-h)^2+k
..
1)-4=A(h)^2+k
2)1=A(1-h)^2)+k
subtract, to eliminate k
3)-5=A(h^2-(1-h)^2)
-5=A(h^2-1+2h-h^2)
-5=A(-1+2h
..
2)1=A(1-h)^2+k
3)8=A(2-h)^2+k
subtract to eliminate k
4)-7=A(1-h)^2-(2-h)^2)
-7=A(1-2h+h^2-4+4h-h^2)
-7=A(-3+2h)
..
-5=A(-1+2h
-7=A(-3+2h)
..
-5=-A+2hA
-7=-3A+2hA
subtract
2=2A
A=1
..
-5=-A+2hA
-5=-1+2h
2h=-4
h=-2
..
1=A(1-h)^2+k (eq 2)
1=1*(1+2)^2+k
1=9+k
k=-8
..
A=1, h=-2, k=-8
Equation of Parabola
y=A(x-h)^2+k
y=(x+2)^2-8
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