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Overview
Grade 10
Develop algebraic and graphical reasoning through the study of relations
13. Determine characteristics of linear relation graphs including intercepts, slope, domain, and range
13.2 Introduction to nonlinear equations
Nonlinear Equations
A linear equation graphs as a straight line; a nonlinear equation graphs as a curve.
What You'll Learn
A linear equation graphs as a straight line, written y = mx + b.
A nonlinear equation graphs as a curve, not a straight line.
y = x squared is nonlinear: it graphs as a parabola.
A variable raised to a power other than 1 usually signals a nonlinear equation.
Straight-line graphing methods (slope, intercepts) only apply to linear equations.
What You'll Practice
1
Graphing parabolas, sideways parabolas, and cubic functions
2
Sketching rational and radical function graphs
3
Using the vertical line test on various nonlinear graphs
4
Determining which nonlinear equations represent functions
Why This Matters
Understanding nonlinear equations prepares you for advanced algebra, precalculus, and calculus courses. The vertical line test and graph recognition skills you develop here are essential tools you'll use throughout higher mathematics to analyze complex relationships and solve real-world problems.
Before You Start — Make Sure You Can:
This Unit Includes
1 Video lesson
Learning resources
Skills
Nonlinear Equations
Vertical Line Test
Graphing
Functions
Parabolas
Rational Functions
Radical Functions
Cubic Functions
MB Curriculum Aligned