The parabola y=3x^2 is translated so that the new vertex is (-2,5). Find the corresponding function.

ummmh,

y = 3(x+2)^2 + 5

To find the corresponding function of the translated parabola, we need to determine how the basic parabola y = 3x^2 has been translated.

First, let's understand the basic parabola y = 3x^2. The vertex form of a parabola is given as y = a(x-h)^2 + k, where (h,k) represents the coordinates of the vertex.

For the parabola y = 3x^2, the vertex is at (0,0) since h = 0 and k = 0.

Now, let's find out how the original parabola has been translated to have a new vertex at (-2,5).

We know that the new vertex is (-2,5), which means that h = -2 and k = 5.

To find the corresponding function, we will substitute these values into the vertex form equation:

y = a(x-h)^2 + k

Substituting h = -2 and k = 5, we get:

y = a(x-(-2))^2 + 5

Simplifying:

y = a(x+2)^2 + 5

Therefore, the corresponding function of the translated parabola is y = a(x+2)^2 + 5.