Question

How do you find the vertex of `y=3x^2 - 12x - 2`?

Answer 1

The vertex is at `(2, -14)`.

Explanation:

To find the vertex of a standard quadratic equation `y = ax^2 + bx + c`, we first use the formula `-b/(2a)` to find the `x` value of the vertex, or `x_v`. We know that `a = 3` and `b = -12`:
`x = -b/(2a) = (-(-12))/(2(3)) = 12/6 = 2`

To find the `y` value of the vertex we simply plug in the `x` value back into the equation and solve for `y`:
`y = 3x^2 - 12x - 2`

`y = 3(2)^2 - 12(2) - 2`

`y = 3(4) - 24 - 2`

`y = 12 - 24 - 2`

`y = -14`

Therefore, the vertex is at `(2, -14)`.

Hope this helps!