SOLUTION: if graph passes through each set of points (-2,-5),(0,-3),((1,4)use them to set up system of equations and calculate A,b,and c.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: if graph passes through each set of points (-2,-5),(0,-3),((1,4)use them to set up system of equations and calculate A,b,and c.      Log On


   

Question 1128564: if graph passes through each set of points (-2,-5),(0,-3),((1,4)use them to set up system of equations and calculate A,b,and c.
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+
(-2,-5)
(1) +-5+=+a%2A%28-2%29%5E2+%2B+b%2A%28-2%29+%2B+c+
(0,-3)
(2) +-3+=+a%2A0%5E2+%2B+b%2A0+%2B+c+
(1,4)
(3) +4+=+a%2A1%5E2+%2B+b%2A1+%2B+c+
--------------------------------------
(1) +4a+-+2b+%2B+c+=+-5+
(2) +c+=+-3+
(3) +a+%2B+b+=+4+
---------------------------------
(3) +b+=+4+-+a+
and
(1) +4a+-+2%2A%28+4+-+a+%29+%2B+%28-3%29+=+-5+
(1) +4a+-+8+%2B+2a+-+3+=+-5+
(1) +6a+=+6+
(1) +a+=+1+
---------------------------------
(3) +b+=+4+-+a+
(3) +b+=+4+-+1+
(3) +b+=+3+
---------------------
The equation is:
+y+=+x%5E2+%2B+3x+-+3+
----------------------------
check:
(-2,-5)
+-5+=+%28-2%29%5E2+%2B+3%2A%28-2%29+-+3+
+-5+=+4+-+6+-+3+
+-5+=+-5+
OK- you can check other points