Lesson 4: Graphing Quadratic Functions

• What does a quadratic graph look like?
• What is the vertex?
• What is the axis of symmetry?
• How do we find the vertex from a table or equation?

Parabola, vertex, axis of symmetry, maximum, minimum, opens up, opens down

CCSS.MATH.9.F.IF.B.4, CCSS.MATH.9.F.IF.C.7

Description: Students create input/output tables for quadratic functions and plot the points, discovering that they form a U-shaped curve (parabola). They identify the vertex (highest or lowest point) and axis of symmetry (line of mirror reflection). Using manipulatives and graphs, they explore how changing coefficients affects the parabola's shape. Purpose: To connect algebraic quadratic expressions to their visual representations and develop understanding of key features. DOK Level: 2-3 (Application)

• Start with simple functions: y = x² before y = x² + 3 or y = 2x²
• For struggling learners: Provide input/output tables; focus on plotting and identifying vertex
• For advanced learners: Explore how coefficients affect the parabola
• Symmetry tools: Use paper folding or mirrors to show axis of symmetry

• Observation: Can students plot points correctly?

• Worksheet: Given a quadratic function, create a table and graph it

• Identification task: Label vertex and axis of symmetry on graphs

• Comparison: Graph two similar functions and describe differences

• Quadratic function cards

• Input/output table templates

• Coordinate plane worksheets

• Mirrors or paper for symmetry exploration

• Resource: Desmos "Graphing Quadratic Functions"