
Part 2 of 2

Question content area top left

Part 1

Use transformations of 

f left parenthesis x right parenthesis equals x squaredf(x)=x2 

to graph the following function.

g left parenthesis x right parenthesis equals negative 3 left parenthesis x plus 3 right parenthesis squared minus 5g(x)=−3(x+3)2−5

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 squaredf(x)=x2.

A.

Stretch the graph horizontally by a factor of 

55.

B.

Stretch the graph vertically by a factor of 

33.

Your answer is correct.

C.

Shift the graph 

33 

unitsunits 

to the 

rightright.

D.

Shift the graph 

55 

unitsunits 

upup.

E.

Shift the graph 

33 

unitsunits 

to the 

leftleft.

Your answer is correct.

F.

Shrink the graph horizontally by a factor of 

55.

G.

Reflect the graph about the​ y-axis.

H.

Shrink the graph vertically by a factor of 

33.

I.

Reflect the graph about the​ x-axis.

Your answer is correct.

J.

Shift the graph 

55 

unitsunits 

downdown.

Your answer is correct.

Part 2

Use the graphing tool to graph the function.

Click to
enlarge
graph

...

Question content area right

Part 1

-10-8-6-4-2246810-10-8-6-4-2246810xy

interactive graph

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 thisView an example

Get more help 

Clear all

Check answer

Now that you’ve identified the correct transformations needed to graph the function \( g(x) = -3(x + 3)^2 - 5 \), the next step is to actually plot the graph using these transformations.

### Steps to Graph \( g(x) = -3(x + 3)^2 - 5 \):

1. **Start with the graph of \( f(x) = x^2 \)**:
   - This is a standard parabola that opens upwards with its vertex at the origin (0, 0).

2. **Apply the Horizontal Shift**:
   - Shift the graph **3 units to the left**. The vertex of the parabola moves from (0, 0) to (-3, 0).

3. **Apply the Vertical Stretch and Reflection**:
   - **Reflect** the graph about the x-axis (it now opens downwards).
   - **Stretch** it vertically by a factor of 3, making the parabola narrower and steeper.

4. **Apply the Vertical Shift**:
   - Shift the graph **5 units down**. The vertex moves from (-3, 0) to (-3, -5).

### Graph Description:
- The vertex of the transformed parabola will be at (-3, -5).
- The parabola opens downward because of the reflection across the x-axis.
- It’s narrower than the standard parabola due to the vertical stretch by a factor of 3.

### How to Use the Graphing Tool:
- **Start by plotting the basic parabola \( f(x) = x^2 \)**.
- **Move the vertex** 3 units to the left to (-3, 0).
- **Reflect the parabola** across the x-axis.
- **Stretch the parabola vertically** so it becomes narrower.
- **Shift the entire graph** 5 units down to place the vertex at (-3, -5).

After applying these transformations, you should see a parabola opening downward, with its vertex at (-3, -5) and stretched vertically.

Would you like more details or have any questions?

Here are some related questions to further explore the topic:

1. What happens to the graph of \( f(x) = x^2 \) if you apply a vertical shrink instead of a stretch?
2. How do you determine the direction of the parabola opening based on the coefficient of \( x^2 \)?
3. How would the graph change if the equation was \( g(x) = -3(x - 2)^2 + 4 \)?
4. What effect does a horizontal stretch have on the width of the parabola?
5. How would you graph the function \( g(x) = 2(x + 3)^2 + 5 \)?

**Tip:** When graphing functions using transformations, always pay attention to the order in which transformations are applied—start with shifts, then stretches/reflections, and finish with vertical shifts.

Learn how to graph the quadratic function g(x) = -3(x + 3)^2 - 5 using transformations of the standard quadratic function f(x) = x^2. Explore the horizontal and vertical shifts, reflections, and stretches involved in transforming the basic parabola. Suitable for high school students studying graphing transformations in quadratic functions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation