Question

Find the vertices of this parabola [(y+2)^2]/4-[x^2]/12=1

Answer 1

This is hyperbola that opens up and down.It follows the format \[\large \frac{(y-k)^2}{b^2} - \frac{(x-h)^2}{a^2}=1\]your formula \[\large \frac{(y-\color{blue}{(-2)})^2}{\color{red}{4}} - \frac{(x-\color{blue}0)^2}{\color{red}{12}} =1\] in order to figure out the vertices, we follow the format \(\large (h,k+b) \ \text{and} \ (h,k-b)\) we can find our "k" from our vertex \(\large (h,k)\) . \[\large v=(h,k)=(0,-2)\] So our vertices will be \[\large (h,k+b)= (0, -2+2) = (0,0)\]\[\large (h, k-b) = (0, -2-2) = (0,-4)\]