On a coordinate plane, two parabolas open up. The solid-line parabola, labeled f of x, goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4). The dashed-line parabola, labeled g of x, goes through (0, 7), has a vertex at (2, 3), and goes through (4, 7).

Question

Which best describes the transformation that occurs from the graph of f(x) = x2 to g(x) = (x – 2)2 + 3?

right 2, up 3
left 2, down 3
right 2, down 3
left 2, up 3
Mark this and return

Answer 1

To understand the transformation from the graph of \( f(x) = x^2 \) to \( g(x) = (x - 2)^2 + 3 \), we can analyze the changes in the equation.

1. Starting point: The graph of \( f(x) = x^2 \) has a vertex at (0, 0).
2. Transformed equation: The equation \( g(x) = (x - 2)^2 + 3 \) indicates:
   • The term \( (x - 2) \) shows a horizontal transformation.
   • The \( -2 \) indicates a shift to the right by 2 units.
   • The \( +3 \) indicates a vertical transformation.
   • The \( +3 \) indicates a shift up by 3 units.

Putting this together, the graph of \( g(x) \) is obtained by transforming the graph of \( f(x) \) to the right by 2 units and up by 3 units.

Thus, the correct answer to describe the transformation is:

right 2, up 3