Chapter 12.6

Graphing quadratic functions: General form VS. Vertex form

What You'll Learn

Identify y-intercepts by setting x equal to zero in the quadratic function
Find x-intercepts by setting y equal to zero and solving the resulting equation
Determine the vertex location using the midpoint of x-intercepts or vertex form
Recognize parabola orientation based on the sign of the leading coefficient
Sketch accurate parabola graphs using intercepts and vertex as key points

What You'll Practice

1

Finding y-intercepts from quadratic functions in general form

2

Solving for x-intercepts by factoring or using square roots

3

Calculating vertex coordinates from both general and vertex forms

4

Sketching complete parabola graphs using all critical points

Why This Matters

Graphing parabolas is essential for visualizing quadratic relationships you'll encounter throughout algebra, calculus, and physics. This skill helps you analyze projectile motion, optimize business profits, and understand how changing variables affect outcomes in real-world scenarios.

Before You Start — Make Sure You Can:

Quadratic function in general form: y = ax^2 + bx + cQuadratic function in vertex form: y = a(x-p)^2 + qConverting from general to vertex form by completing the squareShortcut: Vertex formula

This Unit Includes

2 Video lessons

Skills

Parabolas
Quadratic Functions
Intercepts
Vertex
Graphing
Factoring
Vertex Form
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