SOLUTION: Find the quadratic function that fits the data points (0,0), (6,0) and (8,2)

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Question 535985: Find the quadratic function that fits the data points (0,0), (6,0) and (8,2)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
(0,0)
+0+=+a%2A0+%2B+b%2A0+%2B+c+
+c+=+0+
(6,0)
+0+=+a%2A6%5E2+%2B+b%2A6+%2B+0+
+36a+=+-6b+
+b+=+-6a+
(8,2)
+2+=+a%2A8%5E2+%2B+b%2A8+%2B+0+
+2+=+64a+%2B+8b+
By substitution:
+2+=+64a+%2B+8%2A%28-6a%29+
+2+=+64a+-+48a+
+16a+=+2+
+a+=+1%2F8+
and
+b+=+-6a+
+b+=+-3%2F4+
The function is
+y+=+%281%2F8%29%2Ax%5E2+-+%283%2F4%29%2Ax+
check:
(8,2)
+2+=+%281%2F8%29%2A8%5E2+-+%283%2F4%29%2A8+
+2+=+64%2F8+-+24%2F4+
+2+=+32%2F4+-+24%2F4+
+2+=+8%2F4+
+2+=+2+
OK