Part II: The Answers
154
Answers
1–100
Here’s the graph of y = –(x + 1)
2
+ 6:
71.
y = 3(x – 5)
2
+ 2
To translate the parabola 6 units to the right, you replace x with the quantity
(x – 6). And to translate the parabola 2 units down, you subtract 2 from the original
expression for y:
y
x
x
=
− +
(
) + −
=
−
+
3
6 1
4 2
3
5
2
2
2
(
)
(
)
Another option is simply to count and determine that the new vertex is at (5, 2); then
use the vertex form y = a(x – h)
2
+ k, where the vertex is at the point (h, k).
72.
y = e
−2x
– 5
To compress the graph of y = e
x
horizontally by a factor of 2, replace x with 2x to get
y = e
2x
. To reflect the graph of y = e
2x
across the y-axis, replace x with –x to get y = e
2(–x)
,
or y = e
−2x
. Last, to shift the graph of y = e
−2x
down 5 units, subtract 5 from the right side
of the equation to get y = e
−2x
– 5.
Here’s the graph of y = e
−2x
– 5: