Question 120779
If you are familiar with the quadratic formula, then you know that a quadratic equation of
the generic standard form:
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{{{ax^2 + bx + c = 0}}}
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has as its solutions for x the values that are given by:
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{{{x = -b/(2*a) +- sqrt( b^2-4*a*c )/(2*a) }}}
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The first term on the right side specifies the axis of symmetry. In other words, the axis
of symmetry is given by:
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{{{x = -b/(2*a)}}}
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Now in your given equation, set y equal to zero, and you have the standard form:
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{{{2x^2 - 6x + 5 = 0}}}
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by comparing this equation term by term with the generic form, you can see that a = 2, b = -6,
and c = +5 for this problem. Return to the equation for the axis of symmetry and by substituting
the values for a and b you get:
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{{{x = -b/(2*a) = -(-6)/(2*2) = 6/4 = 3/2}}}
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This tells you that the equation:
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{{{x = 3/2}}}
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is the equation of the axis of symmetry. It is a vertical line through the point {{{3/2}}} on the
x-axis.
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Hope this helps you to see the way you can find the axis of symmetry of a quadratic 
expression.
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