Part 1 of 2

Question content area top left
Part 1
Use transformations of f left parenthesis x right parenthesis equals x squared to graph the following function.
g left parenthesis x right parenthesis equals negative 3 left parenthesis x plus 3 right parenthesis squared minus 5
Question content area bottom left
Part 1
Select all the transformations that are needed to graph the given function using f left parenthesis x right parenthesis equals x squared.
A.
Stretch the graph horizontally by a factor of 5.
B.
Stretch the graph vertically by a factor of 3.
C.
Shift the graph 3 units to the right.
D.
Shift the graph 5 units up.
E.
Shift the graph 3 units to the left.
F.
Shrink the graph horizontally by a factor of 5.
G.
Reflect the graph about the​ y-axis.
H.
Shrink the graph vertically by a factor of 3.
I.
Reflect the graph about the​ x-axis.
J.
Shift the graph 5 units down.
.
.
.
Select all the transformations that are needed to graph the given function using f left parenthesis x right parenthesis equals x squared.Select all the transformations that are needed to graph the given function using f left parenthesis x right parenthesis equals x squared.Select all the transformations that are needed to graph the given function using f left parenthesis x right parenthesis equals x squared.
Help me solve this
View an example
Get more help

To graph the function \( g(x) = -3(x + 3)^2 - 5 \) using transformations of the basic function \( f(x) = x^2 \), we can break down the equation into a sequence of transformations applied to the parent function \( f(x) = x^2 \).

### Step-by-Step Transformation:

1. **Start with the parent function** \( f(x) = x^2 \).

2. **Horizontal Shift**: The term \( (x + 3) \) inside the square indicates a horizontal shift. Specifically, the graph of \( f(x) \) is shifted **3 units to the left**.

3. **Vertical Stretch and Reflection**: The coefficient \( -3 \) outside the squared term affects both the stretching and the reflection:
   - The negative sign indicates that the graph is **reflected about the x-axis**.
   - The coefficient 3 indicates a **vertical stretch by a factor of 3**.

4. **Vertical Shift**: The term \( -5 \) at the end of the function indicates that the entire graph is **shifted 5 units down**.

### Conclusion:

Based on these transformations, the correct options are:

- **B**: Stretch the graph vertically by a factor of 3.
- **E**: Shift the graph 3 units to the left.
- **I**: Reflect the graph about the x-axis.
- **J**: Shift the graph 5 units down.

### Final Answer:
- **B, E, I, J** are the correct transformations needed to graph the function \( g(x) = -3(x + 3)^2 - 5 \).

Would you like more details or have any questions?

Here are some related questions to expand your understanding:

1. How does a horizontal shift differ from a vertical shift in a graph?
2. What effect does a vertical stretch have on the shape of a parabola?
3. How do you determine the direction of a reflection in a graph?
4. What happens to a graph when you apply multiple transformations in a different order?
5. How would the graph change if the equation was \( g(x) = -3(x - 3)^2 - 5 \)?

**Tip:** Always apply horizontal shifts first, then vertical stretches/compressions, reflections, and finally vertical shifts when transforming graphs.

Learn how to graph the quadratic function g(x) = -3(x + 3)^2 - 5 using transformations of the basic function f(x) = x^2. Understand the horizontal and vertical shifts, reflections, and stretches involved in transforming the graph. Suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation