Question

What steps transform the graph of f(x)=x^2 to h(x)=-1/4(x-8)^2+16?

Answer 1

To transform the graph of f(x)=x^2 to h(x)=-1/4(x-8)^2+16, apply a horizontal translation right by 8 units, vertical compression by a factor of 1/4 with a reflection across the x-axis, and then a vertical translation upwards by 16 units.

Step-by-step explanation:

The steps to transform the graph of f(x)=x^2 to h(x)=-1/4(x-8)^2+16 involve several transformations:

1. Horizontal translation: The term (x-8) inside the square indicates that the graph is translated 8 units to the right.
2. Vertical stretch/compression and reflection: The coefficient -1/4 in front of the square indicates a vertical compression by a factor of 1/4 and a reflection across the x-axis.
3. Vertical translation: The +16 at the end of the equation indicates that the graph is translated 16 units upwards.

By combining these transformations, we get the graph of h(x) from the graph of f(x).