This lesson will summarize the family of quadratic functions using the parent function y = x^{2}
Parent function: y = x^{2}
Reflection in x-axis: y = -x^{2}
Stretch by a factor of a: y = ax^{2}
If a > 1, then the graph will stretch or become more narrow than the graph of y = x^{2}
Shrink by a factor of a: y = ax^{2}
If 0 < a < 1, then the graph will shrink or become more wide than the graph of y = x^{2}
(Stretch or Shrink) and reflection in x-axis: y = -ax^{2}
The figure below shows what the graph will look like for a stretch, shrink, or a reflection using y = x^{2} as the parent function. Notice that the blue graph is the parent function or y = x^{2}.
Parent function: y = x^{2}
Vertex form: y = a(x - h)^{2} + k
The vertex is (h, k) and the line x = h is the axis of symmetry.
The graph and vertex of y = ax^{2} shifts h units horizontally and k units vertically.
For k > 0, the graph shifts up
For k < 0, the graph shifts down
For h > 0, the graph shifts to the right
For h < 0, the graph shifts to the left
The figure below shows what the graph will look like for horizontal and vertical shifts using y = x^{2} as the parent function. Notice that the blue graph is the parent function or y = x^{2}.
Sep 17, 23 09:46 AM
Jun 09, 23 12:04 PM