Answer:
Part 1) [tex]y+8=3(x+2)^{2}[/tex] -----> [tex]y=-8.08[/tex]
Part 2) [tex]y-14=-(x-3)^{2}[/tex] ----> [tex]y=14.25[/tex]
Part 3) [tex]y+7.5=2(x+2.5)^{2}[/tex] ----> [tex]y=-7.625[/tex]
Part 4) [tex]y-17=-(x-3)^{2}[/tex] -----> [tex]y=17.25[/tex]
Part 5) [tex]y+7=(x-4)^{2}[/tex] ----> [tex]y=-7.25[/tex]
Part 6) [tex]y-6=-(x-1)^{2}[/tex] ----> [tex]y=6.25[/tex]
Step-by-step explanation:
we know that
The equation of a vertical parabola in vertex form is equal to
[tex]y-k=\frac{1}{4p}(x-h)^{2}[/tex]
where
(h,k) is the vertex
The directrix is
[tex]y=k-p[/tex]
case 1) we have
[tex]y+8=3(x+2)^{2}[/tex]
the vertex is the point (-2,-8)
[tex]\frac{1}{4p}=3[/tex]
[tex]p=\frac{1}{12}[/tex]
The directrix is equal to
[tex]y=-8-\frac{1}{12}=-8.08[/tex]
case 2) we have
[tex]y-14=-(x-3)^{2}[/tex]
the vertex is the point (3,14)
[tex]\frac{1}{4p}=-1[/tex]
[tex]p=-\frac{1}{4}[/tex]
The directrix is equal to
[tex]y=14+\frac{1}{4}=14.25[/tex]
case 3) we have
[tex]y+7.5=2(x+2.5)^{2}[/tex]
the vertex is the point (-2.5,-7.5)
[tex]\frac{1}{4p}=2[/tex]
[tex]p=\frac{1}{8}[/tex]
The directrix is equal to
[tex]y=-7.5-\frac{1}{8}=-7.625[/tex]
case 4) we have
[tex]y-17=-(x-3)^{2}[/tex]
the vertex is the point (3,17)
[tex]\frac{1}{4p}=-1[/tex]
[tex]p=-\frac{1}{4}[/tex]
The directrix is equal to
[tex]y=17+\frac{1}{4}=17.25[/tex]
case 5) we have
[tex]y+7=(x-4)^{2}[/tex]
the vertex is the point (4,-7)
[tex]\frac{1}{4p}=1[/tex]
[tex]p=\frac{1}{4}[/tex]
The directrix is equal to
[tex]y=-7-\frac{1}{4}=-7.25[/tex]
case 6) we have
[tex]y-6=-(x-1)^{2}[/tex]
the vertex is the point (1,6)
[tex]\frac{1}{4p}=-1[/tex]
[tex]p=-\frac{1}{4}[/tex]
The directrix is equal to
[tex]y=6+\frac{1}{4}=6.25[/tex]
