Question 70089
Find the axis of symmetry:
Y= x^2 + 7x + 10 
----------------
You need to put the quadratic in vertex form by completing the square.
This is vertex form: y-k=(x-h)^2 where (h,k) is the vertex.  x=h is 
then the axis of symmetry.
-----------
Rewrite the equation as:
y-10 = x^2+7x
Complete the square on the right side and keep the equation balanced:
y-10+(7/2)^2 = x^2+7x+(7/2)^2
Factor the right side; simplify the left side:
y-10+49/4 = (x+(7/2))^2
y+(9/4) = (x+(7/2))^2
------------
So, -h=7/2
h=-7/2
x=-7/2 is the axis of symmetry
-------------
Here is the graph so you can see the axis of symmetry:
{{{graph(400,300,-10,10,-10,10,x^2+7x+10)}}}

Cheers,
Stan H.