SOLUTION: Write an equation for the parabola in standard form with a vertex of (-1, -2)

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Question 951590: Write an equation for the parabola in standard form with a vertex of (-1, -2)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If the form of the equation is:
+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
+x%5Bv%5D+=+-b%2F%282a%29+
Vertex = ( -1,-2 )
+-1+=+-b%2F%282a%29+
+b+=+2a+
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Now I can say:
+y+=+a%2Ax%5E2+%2B+2a%2Ax+%2B+c+
and, since ( -1,-2 ) is a solution:
+-2+=+a%2A%28-1%29%5E2+%2B+2a%2A%28-1%29+%2B+c+
I'll say +c+=+0+ for this parabola
+-2+=+a%2A%28-1%29%5E2+%2B+2a%2A%28-1%29+%2B+0+
+-2+=+a+-+2a+
+-a+=+-2+
+a+=+2+
and
+b+=+2a+
+b+=+4+
------------
So, the equation is:
+y+=+2x%5E2+%2B+4x+
check:
Does it go through (-1,-2 )?
+-2+=+2%2A%28-1%29%5E2+%2B+4%2A%28-1%29+
+-2+=+2+-+4+
+-2+=+-2+
OK
Here's the plot:
+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+2x%5E2+%2B+4x+%29+