The equation of a parabola is given.y = ½x² + 6x + 24What is the equation of the directrix of the parabola?Enter your answer in the box._________

Answer:The equation of the directrix of the parabola is [tex]y=5.5[/tex]Step-by-step explanation:we know thatThe equation of a vertical parabola in standard form is equal to[tex](x-h)^{2}=4a(y-k)[/tex]where(h,k) is the vertex of the parabolay=k-a is the directrix of the parabolaIn this problem we have[tex]y=\frac{1}{2}x^{2}+6x+24[/tex]Convert to standard form[tex]y-24=\frac{1}{2}x^{2}+6x[/tex][tex]y-24=\frac{1}{2}(x^{2}+12x)[/tex][tex]y-24+18=\frac{1}{2}(x^{2}+12x+36)[/tex][tex]y-6=\frac{1}{2}(x^{2}+12x+36)[/tex][tex]y-6=\frac{1}{2}(x+6)^{2}[/tex]therefore[tex](x+6)^{2}=2(y-6)[/tex] ----> standard formThe vertex is the point (-6,6)[tex]4a=2[/tex][tex]a=\frac{1}{2}=0.5[/tex]The  directrix of the parabola is[tex]y=k-a[/tex][tex]y=6-0.5=5.5[/tex]thereforeThe equation of the directrix of the parabola is [tex]y=5.5[/tex]