Answer:
7. shifted right 8 units
8. shifted left 4 and up 12 units
9. shifted up 8 units
Explanation:
You want to compare the given functions with p(x) = a(x -h)² +k and tell the value and effect of a, h, and k on the vertex.
Transformations
In the equation for p(x) above, the value 'a' represents a vertical scale factor. It expands the graph vertically by the factor 'a'. If a < 0, the graph is reflected across the x-axis.
The values 'h' and 'k' in the equation for p(x) represent a right shift of the graph by 'h' units and a shift up by 'k' units. That is, the graph is translated by (h, k).
7. g(x)
We have h = 8. The graph is shifted right 8 units.
8. h(x)
We have (h, k) = (-4, 12). The graph is shifted left 4 units and up 12 units.
9. f(x)
The values of the transformation parameters are a = -1/2 and k = 8. The vertical compression and reflection do not affect the vertex. The vertex is shifted up 8 units.