Question

Describe how the graph of y= x2 can be transformed to the graph of the given equation.

y = (x + 14)^2 (5 points)

Shift the graph of y = x2 down 14 units.
Shift the graph of y = x2 right 14 units.
Shift the graph of y = x2 left 14 units.
Shift the graph of y = x2 up 14 units.

Answer 1

Explanation:

For y = x², y = 0 when x = 0.

For y = (x + 14)², y = 0 when x = -14.

Notice that the zero of the function has went from 0 to -14, or 14 units to the left.

The answer is "Shift the graph of y = x² left 14 units.".

Answer 2

We conclude that the graph y = x² can be transformed into the graph of the given equation y = (x + 14)² by shifting the graph of y = x² left 14 units.

Explanation:

Please check the attached graph.

• The blue graph is representing the graph of y = x².

• The red graph is representing the graph of y = (x + 14)².

If we carefully analyze the given graph which is attached below, it is clear that the given graph y = (x + 14)² is the transformed image of form f(x+b) of parent graph y = x².

In this graph, the function y = x² has been moved over 14 units to the left.

In other words,

f(x+2) = f(x+14)² means the function f(x) is shifted 14 units to the left.

Therefore, the graph y = x² can be transformed into the graph of the given equation y = (x + 14)² by shifting the graph of y = x² left 14 units.