SOLUTION: For which value of b will the quadratic function below have an x-value of 6 at the minimum ? f(x)=x^2-2bx+7 Any help will be great, thanks.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: For which value of b will the quadratic function below have an x-value of 6 at the minimum ? f(x)=x^2-2bx+7 Any help will be great, thanks.       Log On


   

Question 815212: For which value of b will the quadratic function below have an x-value of 6 at the minimum ?
f(x)=x^2-2bx+7
Any help will be great, thanks.
Found 2 solutions by josmiceli, josgarithmetic:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for the vertex is +x%5Bv%5D+=+-b%2F2a+
when the form of the equation is
+f%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
----------------------
+f%28x%29+=+x%5E2+-+2b%2Ax+%2B+7+
+a+=+1+
+b+=+-2b+ ( different b's )
-----------------------
So,
+x%5Bv%5D+=+6+
+6+=+%28-%28-2b%29%29+%2F+%282%2A1%29+
+6+=+%282b%29%2F2+
+2b+=+12+
+b+=+6+
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So, the equation would be:
+f%28x%29+=+x%5E2+-+2%2A6%2Ax+%2B+7+
+f%28x%29+=+x%5E2+-+12x+%2B+7+
Here's the plot:
+graph%28+400%2C+400%2C+-2%2C+15%2C+-30%2C+5%2C+x%5E2+-+12x+%2B+7+%29+
It looks like when +x=6+, +y=-29+ or so
I'll check:
+y+=+x%5E2+-+12x+%2B+7+
+y+=+6%5E2+-12%2A6+%2B+7+
+y+=+36+-+72+%2B+7+
+y+=+-29+
OK

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Try completing the square to put into standard form. Read the vertex coordinates which will be variabled and compare to the vertex given of x=6 and y = something which you read from the standard form equation.