SOLUTION: what equation is needed for a parabola which passes through points (0,3)(1,6)(-1,8)

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: what equation is needed for a parabola which passes through points (0,3)(1,6)(-1,8)      Log On


   

Question 976776: what equation is needed for a parabola which passes through points (0,3)(1,6)(-1,8)
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
what equation is needed for a parabola which passes through points (0,3)(1,6)(-1,8)
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y = ax^2 + bx + c
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Use the points to make 3 equations, then solve for a, b & c
The 1st one is easy: c = 3
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The general formula is:
+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
( 0,3 )
+3+=+a%2A0%5E2+%2B+b%2A0+%2B+c+
+3+=+c+
----------------
( 1,6 )
+6+=+a%2A1%5E2+%2B+b%2A1+%2B+3+
+a+%2B+b+=+3+
----------------
( -1,8 )
+8+=+a%2A%28-1%29%5E2+%2B+b%2A%28-1%29+%2B+3+
+a+-+b+=+5+
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Add the equations
+a+%2B+b+=+3+
+a+-+b+=+5+
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+2a+=+8+
+a+=+4+
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+a+%2B+b+=+3+
+4+%2B+b+=+3+
+b+=+-1+
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The equation is:
+y+=+4x%5E2+-+x+%2B+3+
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check:
( 0,3 )
+y+=+4x%5E2+-+x+%2B+3+
+3+=+4%2A0%5E2+-+0+%2B+3+
+3+=+3+
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You can check the other 2 points