Question

(b) the graph of $y = x^2$ is shown. translate it to get the graph of $y = (x - 3)^2$.

Explanation:

Step1: Recall Vertex Form Translation

For a quadratic function in vertex form \( y = (x - h)^2 + k \), the graph of \( y = x^2 \) (with vertex at \((0,0)\)) is translated \( h \) units horizontally and \( k \) units vertically. Here, \( y=(x - 3)^2 \) has \( h = 3 \), \( k = 0 \).

Step2: Determine Horizontal Translation

Since \( h = 3 \) (positive), the translation is 3 units to the right. The vertex of \( y = x^2 \) is \((0,0)\); after translation, the vertex of \( y=(x - 3)^2 \) is \((3,0)\). So, we translate the graph of \( y = x^2 \) 3 units to the right.

Answer:

Translate the graph of \( y = x^2 \) 3 units to the right to get the graph of \( y=(x - 3)^2 \).