Podcast
Questions and Answers
What is one description of a parabola involving a point and a line?
What is one description of a parabola involving a point and a line?
Under what condition is the graph of a quadratic function a parabola?
Under what condition is the graph of a quadratic function a parabola?
What is the shape of the graph of a quadratic function with a negative leading coefficient?
What is the shape of the graph of a quadratic function with a negative leading coefficient?
What is the locus of points that are equidistant from the directrix and the focus of a parabola?
What is the locus of points that are equidistant from the directrix and the focus of a parabola?
Signup and view all the answers
When is a parabola the graph of a quadratic function?
When is a parabola the graph of a quadratic function?
Signup and view all the answers
Study Notes
Parabola Definition and Properties
- A parabola can be described as a set of points equidistant from a fixed point (focus) and a fixed line (directrix).
- A quadratic function is graphed as a parabola if its graph opens upward or downward.
Graph of Quadratic Functions
- The graph of a quadratic function with a negative leading coefficient is a parabola that opens downward.
- The shape of the graph of a quadratic function with a positive leading coefficient is a parabola that opens upward.
Locus of Points
- The collection of points equidistant from the directrix and the focus of a parabola forms a parabola itself.
Quadratic Function and Parabola
- A parabola is the graph of a quadratic function if its graph is U-shaped, opening either upward or downward.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
"Test your Knowledge of Parabolas and their Properties" - Take this quiz to assess your understanding of parabolas, including their definitions, focus-directrix relationship, and key properties. This quiz covers the fundamental concepts of parabolas in mathematics.
