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Identify the graph of h(x)=4(x+4)2+6. Then identify t

Identify the graph of h(x)=4(x+4)2+6. Then identify t

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Identify the graph of h(x)=4(x+4)2+6. Then identify the vertex and axis of symmetry.

Here is a transcription and description of the graphs from the image: The image contains four graphs, all depicting parabolas. Each graph consists of a grid with both x and y axes marked. The parabolas are plotted on these coordinate planes. 1. **Top Left Graph:** - The parabola opens upwards with its vertex located at the origin (0,0). - The x-axis ranges from -4 to 4, and the y-axis ranges from -4 to 4. - The graph shows symmetry about the y-axis and passes through points at x = ±2. 2. **Bottom Left Graph:** - Similar to the top left graph, the parabola opens upwards, but it is horizontally shifted. - The x-axis ranges from -4 to 4, and the y-axis remains from -4 to 4. - The vertex is also at the origin, indicating no vertical shift, but the curve is wider. 3. **Top Right Graph:** - The parabola opens upwards with a narrower shape compared to the others. - The x-axis ranges from -4 to 4, with the y-axis extended to 12. - This graph shows symmetry around the y-axis and suggests vertical stretching as it reaches a higher peak. 4. **Bottom Right Graph:** - The parabola opens upwards, similar to the top right graph, but it appears more compressed. - The x-axis ranges from -4 to 4, and the y-axis extends to 12. - The vertex remains at the origin, showing vertical compression leading to a wider spread across the x-axis. These graphs demonstrate how parabolas can vary by orientation, width, and position by adjusting their coefficients in the quadratic equation.
Transcribed Image Text:Here is a transcription and description of the graphs from the image: The image contains four graphs, all depicting parabolas. Each graph consists of a grid with both x and y axes marked. The parabolas are plotted on these coordinate planes. 1. **Top Left Graph:** - The parabola opens upwards with its vertex located at the origin (0,0). - The x-axis ranges from -4 to 4, and the y-axis ranges from -4 to 4. - The graph shows symmetry about the y-axis and passes through points at x = ±2. 2. **Bottom Left Graph:** - Similar to the top left graph, the parabola opens upwards, but it is horizontally shifted. - The x-axis ranges from -4 to 4, and the y-axis remains from -4 to 4. - The vertex is also at the origin, indicating no vertical shift, but the curve is wider. 3. **Top Right Graph:** - The parabola opens upwards with a narrower shape compared to the others. - The x-axis ranges from -4 to 4, with the y-axis extended to 12. - This graph shows symmetry around the y-axis and suggests vertical stretching as it reaches a higher peak. 4. **Bottom Right Graph:** - The parabola opens upwards, similar to the top right graph, but it appears more compressed. - The x-axis ranges from -4 to 4, and the y-axis extends to 12. - The vertex remains at the origin, showing vertical compression leading to a wider spread across the x-axis. These graphs demonstrate how parabolas can vary by orientation, width, and position by adjusting their coefficients in the quadratic equation.
Expert Solution
Step 1: Given Information:

Given that the function is 

                                  h left parenthesis x right parenthesis equals 4 left parenthesis x plus 4 right parenthesis squared plus 6.

To identify the graph, vertex and axis of symmetry of the given function.

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