Lesson Seven: Key Features of Linear and Quadratic Relationships MFM 2P Lesson Seven: Key Features of Linear and Quadratic Relationships Learning Goals: I can tell the difference between between linear and quadratic graphs I can label graphs representing linear and quadratic relationships 2P Currie Unit 1: Key Features

2P Currie Unit 1: Key Features

Which are linear relations? Which are quadratic relations? 2P Currie Unit 1: Key Features

Which represents a linear relationship Which represents a linear relationship? Which represents a quadratic relationship? x y   First Differences -3 16 Second Differences -2 6 -1 1 2 3 x y   First Differences -3 10 Second Differences -2 8 -1 6 4 1 2 3 ½ class do one. The other half do the other. Then share 2P Currie Unit 1: Key Features

Lesson Seven: Key Features of Linear and Quadratic Relationships Terminology Definition How Do I Label It? Graph A Graph B Vertex The maximum or minimum point on the graph. It is the point where the graph changes direction. (x,y)   Axis of symmetry Optimal Value (Min/Max value) x-intercepts (AKA Zeros) y-intercept Opening and Step Pattern 2P Currie Unit 1: Key Features

Graph A Graph B Terminology Definition Label Graph A Graph B Vertex The maximum or minimum point on the graph. It is the point where the graph changes direction. (x,y)   Graph A Graph B 2P Currie Unit 1: Key Features

Graph A Graph B Terminology Definition Label Graph A Graph B Axis of Symmetry   A dotted vertical line that is drawn through the vertex (middle) of the parabola   Graph A Graph B 2P Currie Unit 1: Key Features

Graph A Graph B Terminology Definition Label Graph A Graph B Optimal Value (Min/Max Value)   T he highest (max) y value or the lowest (min)   Graph A Graph B 2P Currie Unit 1: Key Features

Graph A Graph B Terminology Definition Label Graph A Graph B X-Intercepts (AKA Zeros)   Where the parabola crosses the x-axis.   Graph A Graph B 2P Currie Unit 1: Key Features

Graph A Graph B (0,#) Terminology Definition Label Graph A Graph B Y-Intercept   Where the parabola crosses the y-axis. (0,#) Graph A Graph B 2P Currie Unit 1: Key Features

Opening and Step Pattern Terminology Definition Label Graph A Graph B Opening and Step Pattern   Opening – The direction that the parabola opens Step Pattern – The pattern that the y-value increases from the vertex up or down #, #, # Graph A Graph B 2P Currie Unit 1: Key Features

Lesson Seven: Key Features of Linear and Quadratic Relationships MFM 2P Lesson Seven: Key Features of Linear and Quadratic Relationships OR 2P Currie Unit 1: Key Features

MFM 2P Words Definition Rise Run Slope Independent Variable   Run Slope Independent Variable Dependent Variable Initial Value Rate of Change The vertical distance between two points The horizontal distance between two points   The variable whose values we choose. The “x” values. The variable whose values we calculate. The “y” values. The starting amount. The value of the dependent variable when the independent variable is zero. The value of “y” when “x” = 0. Same as slope. 2P Currie Unit 1: Key Features