Select the graph of the function $y = ( x / 3 ) ^ { 2 } - 5$ . Compare the graph of this function with the graph of $y = x ^ { 2 }$
A) Horizontal stretch and vertical shift.
B) Horizontal stretch and vertical shift.
C) Horizontal stretch and vertical shift.
D) Horizontal stretch and vertical shift.
E) Horizontal stretch and vertical shift.

Question

Select the graph of the function $y = ( x / 3 ) ^ { 2 } - 5$ . Compare the graph of this function with the graph of $y = x ^ { 2 }$ 
A) Horizontal stretch and vertical shift. 
B) Horizontal stretch and vertical shift. 
C) Horizontal stretch and vertical shift. 
D) Horizontal stretch and vertical shift. 
E) Horizontal stretch and vertical shift.

Quizplus · Accepted Answer

The graph of $y = ( x / 3 ) ^ { 2 } - 5$ is obtained from the graph of $y = x ^ { 2 }$ by performing a horizontal stretch and a vertical shift. When we substitute $x/3$ in place of $x$ in the equation $y = x^2$ , we get 
$$y = \left(\frac{x}{3}\right)^2 = \frac{x^2}{9}$$
This means that each point on the graph is moved horizontally by a factor of 3. That is, if a point (a,b) lies on the graph of $y=x^2$, the corresponding point on the graph of $y = ( x / 3 ) ^ { 2 } - 5$ is ($3a, b-5$). Therefore, the graph is horizontally stretched by a factor of 3.

Next, we subtract 5 from each y-coordinate, which results in a vertical shift of the graph downward by 5 units.

Thus, the graph of $y = ( x / 3 ) ^ { 2 } - 5$ is obtained from the graph of $y = x ^ { 2 }$ by performing a horizontal stretch by a factor of 3 and a vertical shift downward by 5 units, which matches the graph in choice B.

Select the Graph of the Function y=(x/3)2−5y = ( x / 3 ) ^ { 2 } - 5y=(x/3)2−5

Select the Graph of the Function $y = ( x / 3 ) ^ { 2 } - 5$