SOLUTION: I have posted this question twice, so if someone could please show some mercy and answer this in a detailed, easy to follow step by step process, I would be so very grateful! Fi

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Question 90550: I have posted this question twice, so if someone could please show some mercy and answer this in a detailed, easy to follow step by step process, I would be so very grateful!
Find the axis of symmetry
y=x^2+7x+5

Found 2 solutions by jim_thompson5910, bucky:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
To find the axis of symmetry, use this formula:

From the equation we can see that a=1 and b=7

Plug in b=7 and a=1

Multiply 2 and 1 to get 2

So the axis of symmetry is

Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
The quadratic that you are given is:
.

.
Think of setting y = to zero. If you do, the result will be:
.

.
This is now in the standard quadratic form of:
.

.
and you can apply the quadratic formula to solving it. The quadratic formula tells you that
there are two possible answers for x as follows:
.

.
It's a little hard to see until you think about it, but the answers for x are evenly
distributed about . [That's what the + and - signs of the rest of the
answer for x do for you ... they distribute the values of x evenly on both sides of the line
]. Takes some thought to understand this, but if you can picture it, it
becomes apparent that the vertical line given by is the line of
symmetry ... It goes vertically down the middle of the parabola that you get when you
graph an equation of the form .
.
Back to your problem. Recall that we arranged it in the standard form of:
.

.
and we said that the standard form was:
.

.
By comparing the form from the problem with the standard form we can see that:
.
a = +1
b = +7
c = +5
.
Now recall from above that we said the line of symmetry was given by the equation:
.

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Just plug in the values for "b" and "a" and you get that the line of symmetry is:
.

.
This is the equation of a vertical line through the point on the x-axis.
.
If you graph the original equation of this problem you will get a parabola that drops down
to a low point when x = -7/2 and then rises as x becomes more positive. The axis of
symmetry is the vertical line that goes through that low point on the graph. [In other
problems the axis of symmetry may be the vertical line through the highest point of the
parabola.]
.
Hopefully this will start to make more sense to you as you work more problems of this sort.
Just remember that for a quadratic equation of the form:
.

.
the equation for the line of symmetry is given by . Hope this helps.