Mathematics — first biennium · Lesson
Solving f(x)≥0 means finding the x-values where the graph lies on or above the x-axis.
Prerequisites: Quadratic equations, sign charts and quadratic functions
Goal: Solve quadratic inequalities by reading where the parabola lies above or below the x-axis.
In this lesson: Solve quadratic inequalities by reading where the parabola lies above or below the x-axis.
New concept: Solving a quadratic inequality means finding where the parabola has positive, negative or zero y-values. Its zeros split the x-axis into intervals; the opening direction tells where the graph lies above or below the axis.
How to proceed: Do not memorize 'inside' or 'outside' without checking concavity: choose the graph regions above the x-axis.
You can already assume: Quadratic equations, sign charts and quadratic functions.
Vary a, b and c to observe changes in concavity, vertex position and axis intersections.
With a = 0 the curve loses this family's characteristic shape; also try a non-zero value.
The graph turns the inequality into a question about position relative to the x-axis.
Completed exercises: 0/5 · Correct on first attempt: 0
Do not memorize 'inside' or 'outside' without checking concavity: choose the graph regions above the x-axis.
Data / situation: Solve x²−2x≥0.
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.