Question

Write an equation of the parabola that has the same shape as the graph of f(x)= 2x^2 but with (4, 6) as the vertex. g(x) =

Answer 1

The equation of the parabola with the same shape as f(x) = 2x^2 but with vertex (4, 6) is g(x) = 2(x - 4)^2 + 6.

Step-by-step explanation:

The student has asked to write an equation of a parabola that is shaped like the graph of f(x) = 2x^2 but with a new vertex at (4, 6). The standard equation of a parabola with vertex (h, k) is given by g(x) = a(x - h)^2 + k, where 'a' affects the shape of the parabola, and (h, k) is the vertex. To maintain the same shape as f(x) = 2x^2, we keep 'a' the same and set 'h' and 'k' to 4 and 6, respectively.

Thus, the new equation with vertex (4, 6) is g(x) = 2(x - 4)^2 + 6.