Curriculum placement
Algebra 2. This describes the skill, not a learner estimate.
How many times a line meets a curve
Count distinct real intersections by reducing a system to a quadratic
Problem types
- Count line and parabola intersections
Builds on
- Solving a linear and a nonlinear equation together
- The quadratic formula
- Approximating a solution from a graph · Earlier idea
Solving an equation graphically extends to counting how many times two graphs meet.
Leads to
- A tangent from a point outside a circle · See it applied
A line that meets a circle in exactly one point is tangent to it, which the count of intersections detects.
Related skills
- Zeros and factors of a polynomial · Related idea
The intersections of two graphs are the zeros of the difference of their equations, and the number of zeros is bounded by the degree.
- Fundamental theorem of algebra · Related idea
Counting intersections of a curve and a line counts roots of a polynomial, which the fundamental theorem bounds by its degree.
- Linear equations with letter coefficients · Related idea
A parameter in an equation changes the number of solutions, as it changes the number of intersection points of two curves.
- Calculating with complex numbers · Shared foundations
Open the interactive map to explore lessons and skill connections.