SOLUTION: Consider a quadratic function y =-x^2 +6x+c Rewrite the function in the form y= -(x-h)^2 +k

Algebra ->  Rational-functions -> SOLUTION: Consider a quadratic function y =-x^2 +6x+c Rewrite the function in the form y= -(x-h)^2 +k      Log On


   

Question 1071462: Consider a quadratic function y =-x^2 +6x+c
Rewrite the function in the form y= -(x-h)^2 +k
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
y=-%28x%5E2-6x-c%29
y=-%28x%5E2-6x%2B9-9-c%29 because 9 completes the square.
y=-%28%28x-3%29%5E2-%289%2Bc%29%29
highlight%28y=-%28x-3%29%5E2%2B%28c%2B9%29%29

Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.
This procedure is called "completing the square". 

  -x%5E2+%2B6x%2Bc = 

= %28-x%5E2+%2B+6x%29+%2B+c = 

= %28-x%5E2+%2B+2%2A3%2Ax+-+3%5E2%29 + 3%5E2+%2Bc = 

= -%28x%5E2+-2%2A3%2Ax%2B3%5E2%29 + 9%2Bc = 

= -%28x-3%29%5E2+%2B+%289%2Bc%29.


Solved:  h = 3,  k = 9+c.