Answer:
The order of equation is
[tex]y=\frac{1}{8}x^2-\frac{1}{2}x-\frac{1}{2}[/tex]
[tex]y=-\frac{1}{12}x^2-\frac{7}{6}x-\frac{109}{12}[/tex]
[tex]y=-\frac{1}{32}x^2-\frac{1}{16}x-\frac{289}{32}[/tex]
[tex]y=\frac{1}{20}x^2+\frac{2}{5}x+\frac{29}{5}[/tex]
[tex]y=-\frac{1}{16}x^2+\frac{3}{4}x-\frac{21}{4}[/tex]
[tex]y=\frac{1}{8}x^2+\frac{3}{4}x+\frac{41}{8}[/tex]
[tex]y=-\frac{1}{52}x^2-\frac{4}{13}x-\frac{146}{13}[/tex]
[tex]y=\frac{1}{28}x^2-\frac{5}{14}x+\frac{333}{28}[/tex]
Step-by-step explanation:
If a parabola is defined as
[tex]y=ax^2+bx+c[/tex]
then the directrix of the parabola is
[tex]y=-\frac{b^2}{4a}-\frac{1}{4a}+c[/tex]
1.
The equation of the parabola is
[tex]y=\frac{1}{8}x^2+\frac{3}{4}x+\frac{41}{8}[/tex]
The directrix of the parabola is
[tex]y=-\frac{(\frac{3}{4})^2}{4(\frac{1}{8})}-\frac{1}{4(\frac{1}{8})}+(\frac{41}{8})[/tex]
[tex]y=2[/tex]
Similarly find the directrix of each parabola.
2.
The equation of the parabola is
[tex]y=\frac{1}{20}x^2+\frac{2}{5}x+\frac{29}{5}[/tex]
The directrix of the parabola is [tex]y=0[/tex]
3.
The equation of the parabola is
[tex]y=-\frac{1}{52}x^2-\frac{4}{13}x-\frac{146}{13}[/tex]
The directrix of the parabola is [tex]y=3[/tex]
4.
The equation of the parabola is
[tex]y=-\frac{1}{16}x^2+\frac{3}{4}x-\frac{21}{4}[/tex]
The directrix of the parabola is [tex]y=1[/tex]
5.
The equation of the parabola is
[tex]y=\frac{1}{8}x^2-\frac{1}{2}x-\frac{1}{2}[/tex]
The directrix of the parabola is y=-3.
6.
The equation of the parabola is
[tex]y=-\frac{1}{32}x^2-\frac{1}{16}x-\frac{289}{32}[/tex]
The directrix of the parabola is y=-1.
7.
The equation of the parabola is
[tex]y=-\frac{1}{12}x^2-\frac{7}{6}x-\frac{109}{12}[/tex]
The directrix of the parabola is y=-2.
8.
The equation of the parabola is
[tex]y=\frac{1}{28}x^2-\frac{5}{14}x+\frac{333}{28}[/tex]
The directrix of the parabola is y=4.