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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?
- The focus does not lie on the directrix
- The parabola is the locus of points equidistant from the directrix and the focus (correct)
- The parabola is a plane curve which is mirror-symmetrical
- The parabola is the graph of a quadratic function if its axis is parallel to the y-axis
Under what condition is the graph of a quadratic function a parabola?
Under what condition is the graph of a quadratic function a parabola?
- When the quadratic function has a non-zero leading coefficient (correct)
- When the quadratic function has a positive leading coefficient
- When the quadratic function has a negative leading coefficient
- When the quadratic function has a non-negative leading coefficient
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?
- Hyperbola
- Circle
- Ellipse
- Parabola (correct)
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?
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When is a parabola the graph of a quadratic function?
When is a parabola the graph of a quadratic function?
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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.
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