Answer:
f(x) = 3(x +1)² +2
Explanation:
You want the equation in vertex form of the parabola 3x² after its vertex is translated to (-1, 2).
Vertex form equation
The given form is the "vertex form" of the equation for a parabola. That is, in the form ...
f(x) = a(x -h)² +k
the value of 'a' is the leading coefficient, the scale factor, and the values of h and k are the x- and y-coordinates of the vertex.
Application
Given that the scale factor of the desired parabola is a=3, and the desired vertex is (h, k) = (-1, 2). we can fill in these values in the equation to get ...
f(x) = 3(x -(-1))² +2
f(x) = 3(x +1)² +2