Concord: Graphing Quadratic Equations

Launching a Basketball

Display a picture or video of a basketball shot.

Ask:

• Does the ball travel in a straight line?
• What shape does its path create?
• Where is the highest point?

Explain that many real-world situations create a parabolic path.

Co-Use Activity
Partners discuss examples of parabolas they have seen:

• Basketball shots
• Water fountains
• Fireworks
• Bridges
   

Understanding Parabolas

Introduce:

• Quadratic equation
• Parabola
• Vertex
• X-intercept
• Axis of symmetry

Display a sample graph.

Identify:

• Highest or lowest point (vertex)
• Points where the graph crosses the x-axis (x-intercepts)

Explain:

The vertex is the turning point of a parabola, and x-intercepts show where the graph crosses the x-axis.

Co-Use Activity

Student A identifies the vertex on a graph.

Student B identifies the x-intercepts.

Switch roles.

Exploring the Concord Consortium Interactive

Students access the interactive activity.

Teacher models:

1. Identifying the vertex.
2. Finding x-intercepts.
3. Plotting key points.
4. Sketching the parabola.

Ask:

• What happens when the vertex changes?
• What happens when the parabola opens upward or downward?

Parabola Investigation
 Students complete the interactive activity in pairs.

Activity 1: Find the Vertex
For each graph:

• Identify the vertex.
• Determine whether it is a maximum or minimum.

Activity 2: Find the X-Intercepts

Students identify where the parabola crosses the x-axis.

Activity 3: Graph It

Using the vertex and x-intercepts:

• Sketch the parabola.
• Check answers with the interactive.

Activity 4: Pattern Hunt

Students investigate:

• What happens when the vertex moves up?
• What happens when the vertex moves down?
• What happens when the parabola opens downward?

Co-Use Activity

Partners complete a "Think-Pair-Share."

One partner predicts what will happen.

The other partner tests the prediction using the interactive.

Exit Ticket

Given a graph of a parabola:

1. Identify the vertex.
2. Identify the x-intercepts.
3. State whether the parabola opens upward or downward.
4. Explain how you know.

Success Criteria
Students can:

✓ Identify the vertex.

✓ Find x-intercepts.

✓ Graph a parabola.

✓ Interpret quadratic graphs.

Co-Use Activity

Partners review each other's responses before submitting individual answers.

Real-World Quadratics
Students choose one situation:

A basketball shot
A water fountain
A fireworks display
Students explain:

• Where the vertex would be.
• Where the object starts and lands.
• How does the graph represent the situation?

Co-Use Activity

Partners create a real-world parabola example and share it with another pair.