What is the significance of (h, k)? Today, you will identify the point (h, k) for parabolic, hyperbolic, cubic, absolute value, exponential and square root graphs, and relate the point-slope form of a line to (h, k).

Problem 2-102 Think about the parent graph for parabolas, y = x2. Write the equation of a parabola that will be the same as the parent graph, but shifted four units to the right. y = (x – 4)2

Problem 2-102 (b) Does the strategy you used to move parabolas horizontally also work for other parent graphs? Justify your answer. Yes, the expression can be changed the same way that we changed the quadratic equation.

Problem 2-102 (c) You have learned that the general equation for a parabola is y = a(x – h)2 + k. To move the graph of y = x2 “h” units to the right, you replaced x2 with (x – h)2. Why does replacing x with (x – h) moves a graph to the right.

Parent Graph Tool Kit – Page 98 Obtain copies of the Parent Graph Tool Kit. Work with your team to complete a Tool Kit entry for each of the parent graphs that were displayed in posters by the teams. For each parent graph, complete each of the following: Describe the key characteristics of that family of functions – domain, range, locator point, orientation, etc. Create a transformed equation and complete toolkit entry. For transformation, use: a = 2 or 1/2; h = 3; k = 1 Name of family of functions Write the equation of the parent function Create a table and graph of parent function Write the general equation of the family in graphing form.

Family Names/General Equations Complete for the following: Linear Exponential Growth (b>1) Exponential Decay (0<b<1) Quadratic Square Root Cubic Absolute Value Reciprocal or Hyperbola

“Locator Point: Linear: (h,k) is any point on the line Quadratic: (h,k) is the vertex Cubic: (h,k) is the “center point” – the point where the curve changes Reciprocal: (h,k) is the point where the asymptotes intersect Square Root: (h,k) is the “endpoint” of the curve Absolute Value: (h,k) is the vertex Exponentials: (h,k) helps to locate the curve but can be confusing Maybe use the y-intercept as the “locator point”, but its coordinates are NOT (h,k) OR, shift the asymptote up/down and adjust the graph from there

Graphing Functions With a Stretch Factor “Stretch Before You Run” Cubic Parent Graph Cubic Transformation

Graphing Functions With a Stretch Factor “Stretch Before You Run” Absolute Value Parent Graph Absolute Value Transformation