Question 90550
The quadratic that you are given is:
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{{{y = x^2 + 7x + 5}}}
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Think of setting y = to zero. If you do, the result will be:
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{{{ x^2 + 7x + 5 = 0}}}
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This is now in the standard quadratic form of:
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{{{ax^2 + bx + c = 0}}}
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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:
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{{{x = -(b)/(2*a) +- (sqrt(b^2 - 4*a*c))/(2*a)}}}
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It's a little hard to see until you think about it, but the answers for x are evenly
distributed about {{{-(b)/(2*a)}}}. [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
{{{x = -(b)/(2*a)}}}]. Takes some thought to understand this, but if you can picture it, it
becomes apparent that the vertical line  given by {{{x = -(b)/(2*a)}}} 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 {{{y = ax^2 + bx +c}}}.
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Back to your problem. Recall that we arranged it in the standard form of:
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{{{ x^2 + 7x + 5 = 0}}}
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and we said that the standard form was:
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{{{ax^2 + bx + c = 0}}}
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By comparing the form from the problem with the standard form we can see that:
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a = +1
b = +7
c = +5
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Now recall from above that we said the line of symmetry was given by the equation:
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{{{x = -(b)/(2*a)}}}
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Just plug in the values for "b" and "a" and you get that the line of symmetry is:
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{{{x = -(7)/(2*1) = -7/2 }}}
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This is the equation of a vertical line through the point {{{-7/2}}} on the x-axis.
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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.]
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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:
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{{{y = ax^2 + bx + c}}} 
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the equation for the line of symmetry is given by {{{x = -(b)/(2*a)}}}. Hope this helps.