SOLUTION: Find the quadratic function that includes each set of values. (1, 0), (2, 5), (4, 21)

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find the quadratic function that includes each set of values. (1, 0), (2, 5), (4, 21)      Log On


   

Question 953081: Find the quadratic function that includes each set of values.
(1, 0), (2, 5), (4, 21)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
the general form is:
+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
( 1,0 )
+0+=+a%2A1%5E2+%2B+b%2A1+%2B+c+
(1) +a+%2B+b+%2B+c+=+0+
---------------------
( 2,5 )
+5+=+a%2A2%5E2+%2B+b%2A2+%2B+c+
(2) +4a+%2B+2b+%2B+c+=+5+
----------------------
( 4,21 )
+21+=+a%2A4%5E2+%2B+b%2A4+%2B+c+
(3) +16a+%2B+4b+%2B+c+=+21+
-------------------------
Subtract (1) from (2)
(2) +4a+%2B+2b+%2B+c+=+5+
(1) +-a+-+b+-+c+=+0+
-----------------------
+3a+%2B+b+=+5+
Multiply both sides by +4+
and subtract this result from (3)
+16a+%2B+4b+%2B+c+=+21+
+-12a+-+4b+=+-20+
----------------------
+4a+%2B+c+=+1+
+c+=+-4a+%2B+1+
Plug this into (1)
(1) +a+%2B+b+%2B+-4a+%2B+1+=+0+
also, from above:
+3a+%2B+b+=+5+
+b+=+-3a+%2B+5+
Plug this into (1)
(1) +a+%2B+-3a+%2B+5+%2B+-4a+%2B+1+=+0+
(1) +-6a++=+-6+
(1) +a+=+1+
----------------
+c+=+-4a+%2B+1+
+c+=+-4%2A1+%2B+1+
+c+=+-3+
--------------
+b+=+-3a+%2B+5+
+b+=+-3%2A1+%2B+5+
+b+=+2+
--------------------
Plug these results into:
+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
+y+=+x%5E2+%2B+2x+-+3+
----------------------
check:
( 4,21 )
+21+=+4%5E2+%2B+2%2A4+-+3+
+21+=+16+%2B+8+-+3+
+21+=+21+
You can check the other 2 points