Chapter 12.7

Finding the quadratic functions for given parabolas

What You'll Learn

Apply the vertex form to find quadratic functions when given the vertex and a point
Use the factored form to write equations when given two x-intercepts
Determine the leading coefficient by substituting known points into the equation
Convert between different forms of quadratic equations (vertex and factored forms)
Identify which quadratic form to use based on the given information

What You'll Practice

1

Finding equations using vertex form with vertex and y-intercept

2

Writing quadratic functions from two x-intercepts using factored form

3

Solving for the leading coefficient using additional points on the parabola

4

Working with word problems describing vertex and x-intercept locations

Why This Matters

Finding quadratic functions from graphs is essential for modeling real-world situations where you observe parabolic patterns but need the equation. This skill connects graphical understanding to algebraic representation, preparing you for physics, engineering, and data analysis.

Before You Start — Make Sure You Can:

Quadratic function in vertex form: y = a(x-p)^2 + qConverting from general to vertex form by completing the squareShortcut: Vertex formulaGraphing parabolas for given quadratic functions

This Unit Includes

4 Video lessons
Practice exercises
Learning resources

Skills

Vertex Form
Factored Form
Quadratic Functions
Parabolas
Leading Coefficient
X-intercepts
Graphing
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