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Identify the graph of g(x)=2(x+1)2-3. Then identify the vertex and the axis of symmetry.

Identify the graph of g(x)=2(x+1)2-3. Then identify the vertex and the axis of symmetry.

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 g(x)=2(x+1)2-3. Then identify the vertex and the axis of symmetry. 

The image consists of four graphs, each displaying a parabola on a Cartesian coordinate system. Each graph is overlaid on a grid for precise scaling. 1. **Top Left Graph**: - The parabola opens upwards. - The vertex is at the origin (0,0). - X-axis ranges from -2 to 4. - Y-axis ranges from -2 to 2. 2. **Top Right Graph**: - The parabola opens upwards. - The vertex appears at the x-axis. - X-axis ranges from -2 to 4. - Y-axis extends from -2 to 4. 3. **Bottom Left Graph**: - The parabola opens upwards. - The vertex is at the origin (0,0). - X-axis ranges from -4 to 2. - Y-axis extends from -2 to 2. 4. **Bottom Right Graph**: - The parabola opens upwards. - The vertex appears below the x-axis. - X-axis ranges from -4 to 2. - Y-axis extends from -2 to 6. Each graph features arrows on the axes, indicating the direction of increase. These graphical representations help illustrate how the size and position of the parabola change according to different x and y values.
Transcribed Image Text:The image consists of four graphs, each displaying a parabola on a Cartesian coordinate system. Each graph is overlaid on a grid for precise scaling. 1. **Top Left Graph**: - The parabola opens upwards. - The vertex is at the origin (0,0). - X-axis ranges from -2 to 4. - Y-axis ranges from -2 to 2. 2. **Top Right Graph**: - The parabola opens upwards. - The vertex appears at the x-axis. - X-axis ranges from -2 to 4. - Y-axis extends from -2 to 4. 3. **Bottom Left Graph**: - The parabola opens upwards. - The vertex is at the origin (0,0). - X-axis ranges from -4 to 2. - Y-axis extends from -2 to 2. 4. **Bottom Right Graph**: - The parabola opens upwards. - The vertex appears below the x-axis. - X-axis ranges from -4 to 2. - Y-axis extends from -2 to 6. Each graph features arrows on the axes, indicating the direction of increase. These graphical representations help illustrate how the size and position of the parabola change according to different x and y values.
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