Question

Use transformations of f(x)=x² to graph the following function.

h(x) = (x – 3)² + 6
Select all the transformations that are needed to graph the given function using f(x)=x².
A) Stretch the graph horizontally by a factor of 6.
B) Shift the graph 6 units up.
C) Shift the graph 6 units down.
D) Reflect the graph about the x-axis.
E) Shift the graph 3 units to the right.
F) Shrink the graph vertically by a factor of 3.
G) Shrink the graph horizontally by a factor of 6.
H) Stretch the graph vertically by a factor of 3.
I) Reflect the graph about the y-axis.
J) Shift the graph 3 units to the left.

Answer 1

To graph h(x) = (x – 3)² + 6 using f(x) = x², shift the graph 3 units to the right and 6 units up.

Step-by-step explanation:

To graph the function h(x) = (x – 3)² + 6 using the parent function f(x) = x², we can identify the following transformations:

1. Shift the graph 3 units to the right: This is indicated by the (x - 3) term, which shifts the graph horizontally to the right by 3 units.

2. Shift the graph 6 units up: This is indicated by the +6 at the end, which shifts the graph vertically upwards by 6 units.

3. No other transformations are needed.