Question

the graph of $f(x)=x^2$ was transformed to create $g(x)=(x + 3.5)^2 - 4$. which of these describes this transformation? select two correct answers. (select all that apply.) a horizontal shift to the right 3.5 units a vertical shift down 4 units a vertical stretch a horizontal shift to the left 3.5 units a vertical shift up 4 units a horizontal compression

Explanation:

For a parent function $f(x)=x^2$, the transformed function $g(x)=(x-h)^2+k$ has:

1. Horizontal shift: $h$ determines left/right shifts. Here, $g(x)=(x+3.5)^2-4=(x-(-3.5))^2-4$, so $h=-3.5$, meaning a shift left 3.5 units.
2. Vertical shift: $k$ determines up/down shifts. Here, $k=-4$, meaning a shift down 4 units.

There is no coefficient multiplying the squared term (other than 1), so no stretch/compression.

Answer:

B. A vertical shift down 4 units
D. A horizontal shift to the left 3.5 units