Question

Describe how the graph of y= x^2 can be transformed to the graph of the given equation.

y = (x - 12)^2 + 3 (5 points)

a) Shift the graph of y = x2 up 12 units and then right 3 units.
b) Shift the graph of y = x2 left 12 units and then down 3 units.
c) Shift the graph of y = x2 left 12 units and then up 3 units.
d) Shift the graph of y = x2 right 12 units and then up 3 units.

Answer 1

Shift the graph of y = x2 right 12 units and then up 3 units.

Explanation:

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Answer 2

We conclude that the graph y = x² can be transformed into the graph of the given equation y = (x - 12)²+3 by shifting the graph of y = x² right 12 units and then up 3 units.

Hence, option D is true.

Please check the attached graph.

Explanation:

Given the parent function

y = x²

Given the transformed function

y = (x - 12)²

Horizontal Translation:

The horizontal translation of y = x² is of the form

f(x-h)

so y = y = (x - 12)² means y = x² is shifted 12 right.

Vertical Translation:

y = x²

Then y = x² + b is a vertical translation of y = x²

if b > 0, then y = x² + b is the graph of y = x² 'b' units up.

if b < 0, then y = x² + b is the graph of y = x² 'b' units down.

Thus, y = x² + 3 means the graph y = x² is vertically shifted up by 2 units.

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 - 12)²+3

Therefore, the graph y = x² can be transformed into the graph of the given equation y = (x - 12)²+3 by shifting the graph of y = x² right 12 units and then up 3 units.

Hence, option D is true.