SOLUTION: Rewrite the function f(x) = 2x^2- 8x + 9 in vertex form by completing the square.Also find the minimum value?

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Question 1052409: Rewrite the function f(x) = 2x^2- 8x + 9 in vertex form by completing the square.Also find the minimum value?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
y=ax%5E2%2Bbx%2Bc
y=a%28x%5E2%2B%28b%2Fa%29x%2Bc%2Fa%29

The term to complete the square is %28b%2F%282a%29%29%5E2.

Follow this helpful video:
Change quadratic equation from General form to Standard form

Learn how to do that, and be able to read the minimum or maximum value for "y" from the equation (meaning, read the vertex from the standard form equation).

YOUR answer equation will be f%28x%29=2%28x-2%29%5E2%2B1. The graph has a MINIMUM value for f at the point (2,1).

Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.
Rewrite the function f(x) = 2x^2- 8x + 9 in vertex form by completing the square.Also find the minimum value?
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  2x%5E2-8x+%2B9 =    (if you are not familiar with the procedure "completing the square", 
                    then trace for each my step)


= 2%2A%28x%5E2-4x+%2B+4.5%29 = 2%2A%28x%5E2+-+4x+%2B+4%29+%2B+1 = 2%28x-2%29%5E2+%2B+1.


Completing the square is done.

The most right expression is a vertex form.

The minimum is achieved at x = 2.  The minimum value is 1.