175k views
5 votes
The vertex from of a function is g(x)=(x-3)2+9 how does the graph of g(c) compare to the graph of the function f(x)=x2

User Rowena
by
7.1k points

1 Answer

4 votes

The function g(x) is a quadratic function in vertex form. Its vertex is at (3, 9), and it opens upwards because the coefficient of the squared term is positive.

The function f(x) is also a quadratic function, but in standard form. It opens upwards because the coefficient of the squared term is positive.

Since both functions have a minimum value at the vertex, the graphs of g(x) and f(x) will be similar in shape. However, the vertex of f(x) is at (0,0), so it is shifted to the left of g(x). Also, the y-intercept of f(x) is (0,0), while the y-intercept of g(x) is (0,18).

In summary, the graph of g(x) is the graph of f(x) shifted 3 units to the right and 9 units up.

User Patrick McDermott
by
7.4k points