Project AMP Dr. Antonio Quesada – Director, Project AMP

WORKSHEET Name ______

EXPLORATIONS ON y = a(x+h)n + k ______

______

  1. Parent: y = x Children: y = ax, y = x + h, y = x + k

Variable Parameter / Slope (describe line slant) / x-intercept / y-intercept
a >1
0 < a < 1
-1 < a < 0
a < -1
h > 0
h < 0
k > 0
k < 0

Similarities of Parent & Children Function Differences of Parent & Children Function

  1. Parent: y = IxI Children: y = a IxI, y = Ix + hI, y = IxI + k

Variable Parameter / Slope (describe line slant) / x-intercept / y-intercept
a >1
0 < a < 1
-1 < a < 0
a < -1
h > 0
h < 0
k > 0
k < 0

Similarities of Parent & Children Function Differences of Parent & Children Function

  1. Parent: y = x2 Children: y = ax2, y = (x + h)2, y = x2 + k

Variable Parameter / Vertex / Opening direction / Opening width
a >1
0 < a < 1
-1 < a < 0
a < -1
h > 0
h < 0
k > 0
k < 0

Similarities of Parent & Children Function Differences of Parent & Children Function

  1. Parent: y = x3 Children: y = ax3, y = (x + h)3, y = x3 + k

Variable Parameter / Inflection point / Width / x - intercept
a >1
0 < a < 1
-1 < a < 0
a < -1
h > 0
h < 0
k > 0
k < 0

Similarities of Parent & Children Function Differences of Parent & Children Function

  1. Develop 2 examples using the equation y = a (x + h)n + k for different values of a, h, k, and n (n = 1, 2, or 3). Graph the function and state how the parent function was transformed and/or stretched. Prepare to teach your classmates how to analyze the function graphically and numerically by finding the real zeros of the function.