Mathematics — first biennium · Lesson
A common point of a line and a parabola must satisfy both equations. Equating the two expressions for y gives a quadratic equation; its roots are the x-coordinates of the intersections.
Prerequisites: Quadratic functions, line through two points and quadratic equations
Goal: Find common points of a line and a parabola by connecting the graph to a quadratic equation.
In this lesson: Find common points of a line and a parabola by connecting the graph to a quadratic equation.
New concept: An intersection point of a line and a parabola must satisfy both equations. Substituting the line expression into the parabola gives a quadratic equation; its solutions are the x-coordinates of the real intersections.
How to proceed: The solutions of the resulting equation are only the x-coordinates. To complete the intersection points, you still need their y-coordinates.
You can already assume: Quadratic functions, line through two points and quadratic equations.
The two curves meet at the highlighted points. Algebraically, their x-coordinates are found by setting parabola = line.
Completed exercises: 0/5 · Correct on first attempt: 0
The solutions of the resulting equation are only the x-coordinates. To complete the intersection points, you still need their y-coordinates.
Data / situation: Find the intersections of y=x²−3x+3 and y=2x−1.
ConceptStep separates what is required from what is recommended or useful as reinforcement. Only required prerequisites block your progress.
Relationships: solid line = required · dashed line = recommended · dotted line = reinforcement.