Exploring Key Features of Quadratic Functions

Exploring Key Features of Quadratic Functions

Grade 9 Algebra 1 IB Mathematics Applications and Interpretation 90-Minute Interactive Lesson

Learning Objectives

Identify key features from graphs, tables, equations, and verbal descriptions Transform between standard, vertex, and factored forms Graph parabolas accurately using transformations Translate between multiple function representations Collaborate effectively through Think-Pair-Share activities

Think-Pair-Share: Three Forms of Quadratics

Individual Think: f(x) = x² - 4x + 3 Standard form: f(x) = x² - 4x + 3 Factored form: f(x) = (x - 1)(x - 3) Vertex form: f(x) = (x - 2)² - 1 Pair discussion: What features does each form reveal?

Key Features of Quadratic Functions

Vertex: maximum or minimum point Roots/x-intercepts: where graph crosses x-axis Y-intercept: where graph crosses y-axis Axis of symmetry: vertical line through vertex Domain and range: input and output values Intervals of increase/decrease End behavior: graph direction as x approaches infinity

Exploration Activity: Feature Detective

{"left":"Given: Various quadratic representations\nTask: Identify all key features\nWork in pairs with provided handouts","right":"Use graphs, tables, and equations\nRecord findings on whiteboards\nPrepare to share discoveries"}

Comparing Quadratic Graphs

Technology Integration: Desmos Exploration

Open Desmos graphing calculator Input equations from previous activities Manipulate coefficients: a, b, and c Observe changes in vertex and roots Experiment with transformations Record observations in notebooks

Real-World Application Challenge

A football is kicked and follows the path: h(t) = -16t² + 32t + 6 What does the vertex represent? What do the roots tell us? How high is the ball after 1 second? When does the ball hit the ground?

Guided Practice: Graphing Challenge

Given equation or table of values Identify and plot the vertex Find and mark x and y-intercepts Draw the axis of symmetry Determine domain and range Note intervals of increase/decrease

Reflection and Next Steps

Today I can identify key features of quadratic functions from multiple representations I understand how different forms reveal different information I can apply quadratic functions to solve real-world problems