Question 1085007
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{{{y=ax^2+bx+c}}}

{{{ax^2+bx+c=y}}}

{{{ax^2+bx=y-c}}}

{{{x^2+expr(b/a)x=expr(1/a)y-c/a}}}

Complete the square on the left:

       {{{expr(b/a)*expr(1/2)=b/(2a)}}}
       {{{(b/(2a))^2=b^2/(4a^2)}}}

{{{x^2+expr(b/a)x+b^2/(4a^2)=expr(1/a)y-c/a+b^2/(4a^2)}}}

{{{(x+b/(2a))^2=(1/a)(y-(4ac-b^2)/(4a^""))}}}

Compare to

{{{(x-h)^2=4p(y-k)}}}

{{{h=-b/(2a)}}}, {{{k=(4ac-b^2)/(4a^"")}}}, {{{4p=1/a}}}, {{{p=1/(4a)}}}

The equation of the directrix is 

{{{y = k+p = (4ac-b^2)/(4a^"")+1^""/(4a^"") = (4ac-b^2+1)/(4a^"")}}}

{{{y = (4ac-b^2+1)/(4a^"")}}} <-- equation of directrix

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y=-x^2+3x+8, substitute in above, a=1, b=3, c=8, directrix: y = 6 

y=2x^2+15x+18, substitute a=2, b=15, c=18, directrix: y = -10 

y=x^2+13x+5, substitute a=2, b=13, c=5, directrix: y = -37 

y=-2x^2+4x+8, substitute a=-2, b=4, c=8, directrix: y = 9.975

Edwin</pre>