SOLUTION: I need help please, I could not find an example in the book. Transform the function f(x)=x^2-10x+32 to the form f(x)=c(x-h)^2+k, where c,h,and k are constants, by completing the

Question 182730: I need help please, I could not find an example in the book.
Transform the function f(x)=x^2-10x+32 to the form f(x)=c(x-h)^2+k, where c,h,and k are constants, by completing the square.
Thank-you
Found 2 solutions by vleith, solver91311:
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: COMPLETING THE SQUARE solver for quadratics

Read this lesson on completing the square by prince_abubu, if you do not know how to complete the square.
Let's convert to standard form by dividing both sides by 1:
We have: . What we want to do now is to change this equation to a complete square . How can we find out values of somenumber and othernumber that would make it work?
Look at : . Since the coefficient in our equation that goes in front of x is -10, we know that -10=2*somenumber, or . So, we know that our equation can be rewritten as , and we do not yet know the other number.
We are almost there. Finding the other number is simply a matter of not making too many mistakes. We need to find 'other number' such that is equivalent to our original equation .

The highlighted red part must be equal to 32 (highlighted green part).

, or .
So, the equation converts to , or .

Our equation converted to a square , equated to a number (-7).

There is no number whose square can be negative. So, there is no solution to this equation

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Step 1: Divide the coefficient on the x term by 2.

Step 2: Square the result.

Step 3: Re-write the given constant term as the sum of the results of step 2 and some number. You should now have an x-squared term, an x term, and two constant terms, the first of which is the result of step 2, and the sum of the two is the original constant term.

Step 4: The first three terms are now a perfect square trinomial. Factor it. You should now have a binomial in x squared plus (or minus perhaps) a constant.

In this case c is 1, h will be the second term of the binomial, and k will be the leftover constant.

John

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