SOLUTION: write an quadratic function that has a vertex(-2,-4) and passes through the points (0,0).

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Question 605216: write an quadratic function that has a vertex(-2,-4) and passes through the points (0,0).
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
When the equation is of the form
+ax%5E2+%2B+bx+%2B+c+, the vertex is at
+x%5Bv%5D+=+-b%2F%282a%29+
given:
+-b%2F%282a%29+=+-2+
+-b+=+-4a+
+b+=+4a+
and
+y%5Bv%5D+=+-4+
+-4+=+a%2A%28-2%29%5E2+%2B+b%2A%28-2%29+%2B+c+
+-4+=+4a+-+2b+%2B+c+
and, from above,
+-4+=+4a+-+2%2A%284a%29+%2B+c+
+-4+=+4a+-+8a+%2B+c+
+c+=+4a+-+4+
So far, I have
+y+=+ax%5E2+%2B+%284a%29%2Ax+%2B+4a+-+4+
and this must go through (0,0), so
+0+=+a%2A0+%2B+%284a%29%2A0+%2B+4a+-+4+
+4a+=+4+
+a+=+1+
+b+=+4a+
+b+=+4%2A1+
+b+=+4+
+c+=+4a+-+4+
+c+=+4%2A1+-+4+
+c+=+0+
So, the equation is:
+y+=+x%5E2+%2B+4x+
here's a plot:
+graph%28+400%2C+400%2C+-6%2C+10%2C+-6%2C+10%2C+x%5E2+%2B+4x+%29+