SOLUTION: how do you graph y=x^2+6x+1

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Question 639971: how do you graph y=x^2+6x+1
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+y+=+x%5E2+%2B+6x+%2B+1+
The equation is in the form +y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
First find the axis of symmetry.
That's a vertical line at
+x+=+-b+%2F+%282a%29+ and +y+=+0+
+x+=+-6+%2F+%28+2%2A1+%29+=+-3+
Draw this line, then find the point on the line
where the minimum is, ( -3,y[min] )
+y%5Bmin%5D+=+%28-3%29%5E2+%2B+6%2A%28-3%29+%2B+1+
+y%5Bmin%5D+=+9+-+18+%2B+1+
+y%5Bmin%5D+=+-8+
So the minimum is at (-3,-8) on the axis of symmetry
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Now find the y-intercept at (0,y)
+y+=+0%5E2+%2B+6%2A0+%2B+1+
+y+=+1+
The y-intercept is at (0,1)
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You can plug any values you want into x and
get the value of y
I'll say +x+=+-6+
+y+=+%28-6%29%5E2+%2B+6%2A%28-6%29+%2B+1+
+y+=+36+-+36+%2B+1+
+y+=+1+
So the point (-6,1) lies on the graph
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Here's the plot:
+graph%28+400%2C+400%2C+-10%2C+3%2C+-10%2C+10%2C+x%5E2+%2B+6x+%2B+1+%29+