Question

Describe the transformations of the function from g(x)=x² to h(x)=-(x-3)²+4.

Answer 1

The function g(x) = x² is transformed to h(x) = -(x-3)²+4 by reflecting the graph across the x-axis, shifting it 3 units to the right, and moving it 4 units up.

Step-by-step explanation:

The function g(x) = x² represents a quadratic function with a vertex at the origin. To transform this function to h(x) = -(x-3)²+4, we can identify the different transformations:

1. The negative sign in front of (x-3) reflects the graph across the x-axis.
2. The -3 inside the parentheses shifts the graph 3 units to the right.
3. Finally, the +4 at the end of the function moves the graph 4 units up.

By applying these transformations to the original function g(x)=x², we obtain the function h(x) = -(x-3)²+4.