Answered

IDNLearn.com offers a user-friendly platform for finding and sharing answers. Discover prompt and accurate answers from our experts, ensuring you get the information you need quickly.

Find the vertex, focus, and directrix. y = 1/24(x+1)² - 3. 

Sagot :

Lilithidn
[tex]y = \frac{1}{24}(x+1)^2 - 3\\\\y+3 =\frac{1}{24}(x+1)^2\ \ / *24\\\\ (x+1)^2 = 24(y+3)[/tex]

This   is  an  equation  of  a  parabola  that  opens  upwards.

[tex]Its \ standard \ form: \\(x-h)^2=4p(y-k)\\ (h,k)=(x,y) \ coordinates \ of \ the \ vertex\\\ (h,k)=(-1,-3) \\\\axis \ of \ symmetry: \ x= -1\\ \\4p=24\ \ /:4\\p=6[/tex]

[tex]focus:(h,k+p)=(-1,-3+6)=(-1,3) \\ \\directrix: \ y=k-p=-3-6=-9[/tex]


View image Lilith
Kate200468idn
[tex] the\ equation\ in\ the\ form\ (x-h)^2=4p(y-k)\ is \ a\ parabola\\with\ a\ vertex\ at\ \ (h,\ k), \\a\ focus\ at\ \ (h,k+p)\\\ and\ a\ directrix\ \ y = k - p \\\\ y = 1/24(x+1)^2 - 3\ \ \ \ \Rightarrow\ \ \ y+3 = 1/24(x+1)^2\ /\cdot24\\\\ 24\cdot(y+3)=(x+1)^2\\\\(x+1)^2=4p(y+3)\ \ \Rightarrow\ \ 4p=24\ \ \Rightarrow\ \ p=6\ \ \ and\ \ \ h=-1,\ k=-3\\\\the\ vertex:\ \ \ (h;\ k)=(-1;\ -3)\\\\the\ focus:\ \ \ (h;\ k+p)=(-1;\ -3+6)=(-1;\ 3)\\\\the\ directrix:\ \ \ y=k-p\ \ \ \Rightarrow\ \ \ y=-3-6=-9 [/tex]
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Your search for solutions ends here at IDNLearn.com. Thank you for visiting, and come back soon for more helpful information.