Question

What is the vertex of `3y= 7(x+15)^2 +12`?

Answer 1

vertex: `color(blue)(""(-15,+4))`

Explanation:

The general vertex form is
`color(white)("XXX")y=color(green)(m)(x-color(red)(a))^2+color(blue)(b)`
with vertex at `(color(red)(a),color(blue)(b))`

The given `3y=7(x+15)^2+12`
can be converted into the general vertex form by dividing both sides by `3` and replacing the `+15` by `-(-15)`
`color(white)("XXX")y=color(green)(7/3)(x-color(red)(""(-15)))^2+color(blue)(4)`
for the equation of a parabola with vertex at `(color(red)(-15),color(blue)(4))`

Here is a graph of the original equation for verification purposes:
graph{3y-(7(x+15)^2+12) = 0 [-17.037, -10.104, 2.232, 5.693]}