Answer:
f(x) is a parabola with a vertex at (0, 0) that opens up
g(x) is a parabola with a vertex at (0, 2) that opens up
Explanation:
Quadratic equation:
The graph of a quadratic equation is a parabola. The value of
determines its orientation.
If
then the parabola opens upwards and its vertex is its minimum point.
If
then the parabola opens downwards and its vertex is its maximum point.
Given:
⇒ g(x) = f(x) + 2
So the transformation of f(x) to g(x) is an upward shift of 2 units, or
a translation of f(x) by the vector
.
Therefore, the y-coordinate of the vertex of g(x) will be 2 units more than the y-coordinate of the vertex of f(x).
Therefore,
- f(x) is a parabola that opens upwards with a vertex at (0, 0)
- g(x) s a parabola that opens upwards with a vertex at (0, 2)