5 Questions
What is one description of a parabola involving a point and a line?
The parabola is the locus of points equidistant from the directrix and the focus
Under what condition is the graph of a quadratic function a parabola?
When the quadratic function has a non-zero leading coefficient
What is the shape of the graph of a quadratic function with a negative leading coefficient?
Parabola
What is the locus of points that are equidistant from the directrix and the focus of a parabola?
A straight line
When is a parabola the graph of a quadratic function?
When its axis is parallel to the y-axis
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.
"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.
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