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Overview
Foundations of Mathematics and Pre-Calculus 10
3. Functions and relations: connecting data, graphs, and situations
3.15 Introduction to quadratic functions
Introduction to Quadratic Functions
Get a clear introduction to quadratic functions: what makes a function quadratic, its standard form, and how its graph creates a parabola.
What You'll Learn
Identify a quadratic function by its highest power of x squared with a nonzero leading coefficient
Recognize the standard form y equals a x squared plus b x plus c and what each letter controls
Compare quadratic graphs to linear graphs to see why parabolas curve instead of forming straight lines
Locate the vertex and axis of symmetry as the key reference points of a parabola
Determine whether a parabola opens upward or downward based on the sign of the leading coefficient a
What You'll Practice
1
Finding y-intercepts by substituting x = 0
2
Calculating x-intercepts by setting y = 0 and solving
3
Determining vertex position using x-intercepts or vertex form
4
Sketching parabolas by plotting intercepts and vertex
Why This Matters
Understanding quadratic functions is essential for algebra and beyond. You'll use these skills to model real-world situations like projectile motion, optimize business profits, and solve engineering problems. Mastering vertex and intercept identification builds the foundation for calculus and advanced math courses.
This Unit Includes
2 Video lessons
Learning resources
Skills
Quadratic Functions
Parabolas
Vertex
Intercepts
Factoring
Graphing
Vertex Form
BC Curriculum Aligned