Question

4. Use the functions below to complete Parts I and II.

f(x) = x2 g(x) = (x – 3)2 + 2
Part I: The graph of f(x) is shown below. g(x) has the same shape as f(x), but is shifted as described by the equation g(x) = (x – 3)2 + 2. Draw and label the graph of g(x) on the same grid as f(x). (3 points)
HINT: Making a table of values for g(x) may help you to graph it.

Part II: Describe how the graph of g(x) relates to the graph of its parent function, f(x). (3 points)
HINT: Think about how f(x) was shifted to get g(x).

Answer 1

The answer as follows

Explanation:

Part I:

The graph of f(x) is a parabola with its vertex at the origin, opening upward.

To graph g(x), we can start by shifting f(x) 3 units to the right and 2 units up, according to the equation g(x) = (x - 3)² + 2. This means that the vertex of g(x) will be at the point (3, 2).

We can create a table of values for g(x) to plot some points and draw the graph:

| x | g(x) |

|----|------|

| 0 | 11 |

| 1 | 8 |

| 2 | 5 |

| 3 | 2 |

| 4 | 5 |

| 5 | 8 |

| 6 | 11 |

Using these points, we can draw the graph of g(x) as a parabola that has the same shape as f(x), but is shifted to the right by 3 units and up by 2 units:

Part II:

The graph of g(x) is the graph of its parent function, f(x), shifted 3 units to the right and 2 units up. This means that every point on the graph of g(x) is 3 units to the right and 2 units up from the corresponding point on the graph of f(x).

In other words, the transformation that was applied to f(x) to get g(x) is a horizontal shift to the right by 3 units and a vertical shift up by 2 units. This is reflected in the equation g(x) = (x - 3)² + 2.