SOLUTION: Find the vertex of f(x)=-3x^2+12x-11 by keeping it in standard form (using formula)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the vertex of f(x)=-3x^2+12x-11 by keeping it in standard form (using formula)      Log On


   

Question 1024561: Find the vertex of f(x)=-3x^2+12x-11 by keeping it in standard form (using formula)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If the form is:
+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+, the formula is:
+x%5Bv%5D+=+-b%2F%282a%29+
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+y+=+-3x%5E2+%2B+12x+-+11+
+a+=+-3+
+b+=+12+
+x%5Bv%5D+=+-12%2F%28+2%2A%28-3%29+%29+
+x%5Bv%5D+=+2+
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Plug this result back into equation to get +y%5Bv%5D+
+y%5Bv%5D+=+-3%2A2%5E2+%2B+12%2A2+-+11+
+y%5Bv%5D+=+-3%2A4+%2B+24+-+11+
+y%5Bv%5D+=+24+-+23+
+y%5Bv%5D+=+1+
------------
The vertex is at ( 2,1 )
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Here's the plot:
+graph%28+400%2C+400%2C+-3%2C+7%2C+-7%2C+3%2C+-3x%5E2+%2B+12x+-+11+%29+