Answer:
I guess that we want to find the equation for each case.
First, let's define the translations:
Horizontal translation.
For a function f(x), an horizontal translation of N units is written as:
g(x) = f(x + N)
if N > 0, the translation is to the left
if N < 0, the translation is to the right.
Vertical translation:
For a function f(x), a vertical translation of N units is written as:
g(x) = f(x) + N
if N > 0, the translation is upwards
if N < 0, the translation is downwards.
Now that we know these, we can find the equations for each case:
1. the graph of y = x² is moved five units upward
the graph is given by a vertical translation of 5 units upward.
y = x^2 + 5
2 the graph of y = 5x² is moved six units to the left
this is:
y = 5*(x + 6)^2
3: the graph of y = -2x² is moved seven units downward
this is:
y = -2x^2 - 7
4: the graph of y = -x² is moved two units to the left and four units downward
now we have two translations, first 4 units to the left and then 4 units downwards, this gives:
y = -(x + 4)^2 - 4
5: the graph of y = -3x² is moved two units to the right
Remember that to move the graph to the right, we need to have N negative, then:
y = -3(x - 2)^2