Question

Find the vertical asymptotes. 2x2 + 7x + 6 y = 3x2 + 10x - 8 * = [ [?], x=​

Answer 1

`-(77)/(24)`

Explanation:

1. rewrite the equation in standard form:
`4\cdot (3)/(2)\left(y-\left(-(41)/(24)\right)\right)=\left(x-\left(-(3)/(2)\right)\right)^2`

2. find (h,k), the vertex. the vertex is
`\left(h,\:k\right)=\left(-(3)/(2),\:-(41)/(24)\right)`

3. find the 'focal length' of the parabola - the focal length is the distance between the vertex and the focus. from the vertex we can see that the focal length, p, = 3/2

4. Parabola is symmetric around the y-axis and so the asymptote is a line parallel to the x-axis, a distance p from the
`\left(-(3)/(2),\:-(41)/(24)\right)` y coordinate which is at
`-(41)/(24)\right)`. Set up the equation:

`y=-(41)/(24)-p`

5. substitute and solve:

`y=-(41)/(24)-(3)/(2)`

`y = -(77)/(24)`

hope this helps, ask me questions if you still don't understand.