SOLUTION: Express the function {{{ f(x)=2x^2 -8x+3 }}} in the form {{{ f(x)=a(x-h)^2 +k }}} by completing the square

Algebra ->  Rational-functions -> SOLUTION: Express the function {{{ f(x)=2x^2 -8x+3 }}} in the form {{{ f(x)=a(x-h)^2 +k }}} by completing the square      Log On


   

Question 287926: Express the function +f%28x%29=2x%5E2+-8x%2B3+ in the form +f%28x%29=a%28x-h%29%5E2+%2Bk+ by completing the square
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E2-8x%2B3 Start with the given expression.


2%28x%5E2-4x%2B3%2F2%29 Factor out the x%5E2 coefficient 2. This step is very important: the x%5E2 coefficient must be equal to 1.


Take half of the x coefficient -4 to get -2. In other words, %281%2F2%29%28-4%29=-2.


Now square -2 to get 4. In other words, %28-2%29%5E2=%28-2%29%28-2%29=4


2%28x%5E2-4x%2Bhighlight%284-4%29%2B3%2F2%29 Now add and subtract 4 inside the parenthesis. Make sure to place this after the "x" term. Notice how 4-4=0. So the expression is not changed.


2%28%28x%5E2-4x%2B4%29-4%2B3%2F2%29 Group the first three terms.


2%28%28x-2%29%5E2-4%2B3%2F2%29 Factor x%5E2-4x%2B4 to get %28x-2%29%5E2.


2%28%28x-2%29%5E2-5%2F2%29 Combine like terms.


2%28x-2%29%5E2%2B2%28-5%2F2%29 Distribute.


2%28x-2%29%5E2-5 Multiply.


So after completing the square, 2x%5E2-8x%2B3 transforms to 2%28x-2%29%5E2-5. So 2x%5E2-8x%2B3=2%28x-2%29%5E2-5.


So f%28x%29=2x%5E2-8x%2B3 is equivalent to f%28x%29=2%28x-2%29%5E2-5.


So the equation f%28x%29=2%28x-2%29%5E2-5 is now in vertex form f%28x%29=a%28x-h%29%5E2%2Bk where a=2, h=2, and k=-5