2-6: Writing Quadratic Equations

​Objective 2-6: 🎯 I can write a quadratic equation from given features or points.
Sub-Objective: 🧩 I can use vertex form y = a(x – h)² + k and standard form y = ax² + bx + c to model quadratics from graphs, vertices, and points.
Warm-Up:
1️⃣ Review: Describe the transformations of
y = –2(x – 3)² + 4.
2️⃣ Lead-In: If a quadratic has vertex (3, 4) and passes through (5, 12), what equation could model it?

​Today’s Plan:
Warm-Up & Review (Transformations)
Notes: From Features
→ Equation Mild
→ Medium Practice
Think-Pair-Share: Discussion CYU Check & Reflection

​Warm-Up:
1️⃣ Review: Describe the transformations of
y = –2(x – 3)² + 4.



2️⃣ Lead-In: If a quadratic has vertex (3, 4) and passes through (5, 12), what equation could model it?

​Concept Overview
Connecting 2-5 → 2-6 In 2-5 we learned what a, h, and k do to a graph.

In 2-6 we learn how to find them when we know information about the graph.

Key Formulas:
1. Vertex Form: y = a(x – h)² + k
- Vertex → (h, k)
- Use another point to find 'a'.

2. Standard Form: y = ax² + bx + c
- Use three points to create and solve a system

​Mild:
Example 1 – Vertex Given
Find the equation of a parabola with vertex (1, –2) and point (3, 6).

​Mild:

Try It: Write the equation of the quadratic with vertex (–2, 3) and point (0, 7).

​Think-Pair-Share Prompt #1:

Partner A: Explain your steps for finding a.

Partner B: Describe how you know the graph opens up or down.

Together: Compare your answers and verify the vertex.

​Medium:

Example 2 – From a Graph or Table

A quadratic function passes through (–1, 5), (0, 2), and (2, 10). Find its equation in standard form.

​Medium (Student Try)

Try It:
A quadratic function passes through (–2, 8), (0, 4), and (2, 8). Find its equation in standard form.

Steps Hint:
1. y = ax² + bx + c
2. Plug in each point → 3 equations
3. Solve for a, b, c

​CYU:
Mild:
1. Write the equation of the quadratic function with vertex (2, –1) and point (0, 7).

Medium:
2. Write the equation of the quadratic function in standard form that passes through (–1, 6), (0, 3), (2, 9).

Spicy (Application):
3. A firework is launched from the ground and reaches its maximum height of 64 m after 4 seconds. It lands back on the ground after 8 seconds. Write an equation to model the height of the firework over time.