Curriculum placement
Algebra 2. This describes the skill, not a learner estimate.
Approximating a solution from a graph
Approximate intersections using graphs tables and successive refinement
Problem types
- Solve two functions with a table of values
- Count the solutions of a rational expression equal to an absolute value
Builds on
- A graph as the solution set
- Graphs of quadratic functions
- Where a line meets a parabola · Earlier idea
Reading shared points of a line and a parabola extends to any equation f(x) = g(x): the solutions are the inputs where the two outputs match. A table of values locates them.
Leads to
- How many times a line meets a curve · Extend the idea
Solving an equation graphically extends to counting how many times two graphs meet.
- Solving trigonometric equations · See it applied
The solutions of a trigonometric equation are the points where the sine graph meets a horizontal line, so there are many of them.
Related skills
- Solving a linear and a nonlinear equation together · Related idea
Substitution gives exact intersections when the equation can be solved by factoring. A table of values approximates intersections that algebra cannot give simply.
- Solving radical equations · Related idea
Extraneous roots appear when squaring an equation, and a graph shows which solutions are real intersections.
- Solving rational equations · Related idea
Solutions of a rational equation are the x-values where two rational graphs meet.
- Comparing functions given in different forms · Shared foundations
- Shifts, stretches, and reflections of graphs · Shared foundations
Open the interactive map to explore lessons and skill connections.