Question

A quadratic function y=f(x) is plotted on a graph, and the vertex of the resulting parabola is (4, -6). What is the vertex of the function defined as g(x)=f(x)+4?

a) (0, -2)
b) (4, -2)
c) (4, -10)
d) (8, -6)

Answer 1

To find the vertex of the function g(x)=f(x)+4 when the vertex of f(x) is at (4, -6), add 4 to the y-coordinate of the vertex of f(x), keeping the x-coordinate the same. The new vertex is (4, -2), option b.

Step-by-step explanation:

If a quadratic function y=f(x) has its vertex at (4, -6), we can determine the vertex of g(x)=f(x)+4 by simply adding 4 to the y-coordinate of the vertex of f(x). The transformation represented by 'plus 4' shifts the graph of f(x) vertically upwards by 4 units. This means the x-coordinate of the vertex will remain the same, while the y-coordinate will increase by 4. Therefore, the vertex of g(x) will be (4, -2), which corresponds to option b.