Question

Write the given function in vertex form by completing the square:
y=x^2+9x+2

Answer 1

Ok! So
\[x^2+9x+k\]
How do you find k so that this is a complete square?

Answer 2

\[x^2+9x+(\frac{9}{2})^2=(x+\frac{9}{2})^2\]
This will always work if the coefficient of x^2 is 1
Just divide the number in front of x by 2 then square like I did above

Answer 3

Now back to finding the vertex form!

Answer 4

\[y=x^2+9x+(\frac{9}{2})^2-(\frac{9}{2})^2+2\]
Whatever I add in I must also take out

Answer 5

The form we are aiming for by the way is:
\[y=a(x-h)^2+k\]

Answer 6

So You should be able to write that one part (x^2+9x+(9/2))^2) as a complete square which I at the beginning of this thread

Answer 7

And then all you have to do after simplify if you can such as the -(9/2)^2+2 part

Answer 8

thankyou!