2-5: Transformations of Quadratics

🗓️ Today’s Plan:

1. Warm-Up + Review

2. Notes: Parent Function & Transformations

3. Mild → Medium Guided Practice

4. Think-Pair-Share Discussion

5. Check-Your-Understanding (CYU)

🎯 Objective: I can describe and perform transformations of the parent quadratic.

• Sub-Objective: I can identify how changes in a, h, and k affect the graph of y = a(x-h)² + k.
  

🔥 Warm-Up:

1️⃣ Review: Identify the vertex and axis of symmetry of y = (x - 2)² + 1.

2️⃣ Lead-In: Predict how y = 2(x - 2)² + 1 compares to y = (x - 2)² + 1.

📅 AGENDA — Integrated Math II

​🔥 Warm-Up:

1️⃣ Review: Identify the vertex and axis of symmetry of y = (x - 2)² + 1.

2️⃣ Lead-In: Predict how y = 2(x - 2)² + 1 compares to y = (x - 2)² + 1.

​a → vertical stretch/compression/flip h → horizontal shift k → vertical shift

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​Mild – Example 1
Describe how the graph of each function changes from y = x².
a. y = (x - 4)²
b. y = x² + 3
c. y = -2(x + 1)²

Open Ended

Describe the transformation from y = x² to each new function.
a. y = (x + 2)²
b. y = -x² + 5
c. y = ½(x - 3)²

​Think-Pair-Share Prompt:
1. “What does 'a' tell you about the graph’s shape or direction?”

2. “If we compare (x - 3)² and (x + 3)², what’s different?”

​Medium – Example 2
Write the quadratic equation that matches each description:
a. Vertex at (2, –3), opens upward, passes through (3, –2).
b. Vertex at (–1, 4), opens downward, narrower than y = x².

Steps:
Step 1: Start with y = a(x-h)² + k
Step 2: Substitute vertex → (h, k)
Step 3: Plug in point → solve for a

​✅ Think-Pair-Share Prompt:
1. “How does knowing the vertex help you write the equation faster?”


2. “What does the point tell us about the stretch or compression?”

​Error Analysis:
A student wrote y = (x + 3)² + 2 for a vertex at (3, 2). What went wrong? How can we fix it?

​CYU (Check Your Understanding)
Mild:
1. Describe the transformation of y = –(x – 4)² + 2.
Medium:
2. Write the quadratic with vertex (2, –3) passing through (1, 0).
Spicy:
3. A ball is thrown upward from ground level and reaches a max height at x = 3 seconds, y = 9 meters. Write a quadratic to model its path.