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Identify the graph of y=0.4(x-1)2. Then identify the vertex and axis of symmetry.

Identify the graph of y=0.4(x-1)2. Then identify the vertex and 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 y=0.4(x-1)2. Then identify the vertex and axis of symmetry.

The image presents four graphs of quadratic functions displayed on a coordinate plane with a grid. Each graph features a parabolic curve, and there is a selection bubble next to each one. 1. **Top Left Graph:** - This is a standard upward-opening parabola centered at the origin. - The vertex of the parabola is at the point (0, 0). - The curve passes through points approximately (-2, 4) and (2, 4). - The parabola is symmetric with respect to the y-axis and increases as it moves away from the vertex. 2. **Top Right Graph:** - This parabola is narrow and opens upward. - The vertex is slightly above the x-axis, approximately at point (0, -2). - The arms of the parabola point upwards and converge more steeply than the other graphs. 3. **Bottom Left Graph:** - Similar to the top left graph, this parabola opens upwards. - The vertex is also at the origin (0, 0). - The parabola is symmetric about the y-axis and passes through points (-2, 4) and (2, 4). 4. **Bottom Right Graph:** - This is a downward-opening parabola. - The vertex is at the origin (0, 0). - The parabolic curve symmetrically descends on both sides as it moves away from the vertex. - It crosses the y-axis at the origin and appears symmetric across this axis. Each graph is plotted on a grid with axes labeled from -4 to 4 for both x and y. The grid helps to visualize the symmetry and dimensions of the parabolas.
Transcribed Image Text:The image presents four graphs of quadratic functions displayed on a coordinate plane with a grid. Each graph features a parabolic curve, and there is a selection bubble next to each one. 1. **Top Left Graph:** - This is a standard upward-opening parabola centered at the origin. - The vertex of the parabola is at the point (0, 0). - The curve passes through points approximately (-2, 4) and (2, 4). - The parabola is symmetric with respect to the y-axis and increases as it moves away from the vertex. 2. **Top Right Graph:** - This parabola is narrow and opens upward. - The vertex is slightly above the x-axis, approximately at point (0, -2). - The arms of the parabola point upwards and converge more steeply than the other graphs. 3. **Bottom Left Graph:** - Similar to the top left graph, this parabola opens upwards. - The vertex is also at the origin (0, 0). - The parabola is symmetric about the y-axis and passes through points (-2, 4) and (2, 4). 4. **Bottom Right Graph:** - This is a downward-opening parabola. - The vertex is at the origin (0, 0). - The parabolic curve symmetrically descends on both sides as it moves away from the vertex. - It crosses the y-axis at the origin and appears symmetric across this axis. Each graph is plotted on a grid with axes labeled from -4 to 4 for both x and y. The grid helps to visualize the symmetry and dimensions of the parabolas.
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