Parabolas are U-shaped curves defined by a quadratic equation. Key features include the vertex (the turning point), the focus (a point inside the curve), and the directrix (a line outside the curve). Understanding these features allows you to graph parabolas and solve related problems. The standard form equations help us identify these features easily.
Match each term with its correct definition:
| Term | Definition |
|---|---|
| 1. Vertex | A. The line perpendicular to the directrix and passing through the focus. |
| 2. Focus | B. The U-shaped curve defined by a quadratic equation. |
| 3. Directrix | C. The turning point of a parabola. |
| 4. Axis of Symmetry | D. A fixed point on the interior of a parabola that defines the curve. |
| 5. Parabola | E. A line that defines the parabola. |
Match the terms with the definitions. (Example: 1-C, 2-D, etc.)
Complete the following paragraph using the words provided: vertex, axis of symmetry, focus, directrix, parabola.
The _________ is a U-shaped curve. The turning point of the curve is called the _________. The _________ is a point inside the curve, and the _________ is a line outside the curve. The _________ divides the _________ into two symmetrical halves.
Explain how the distance between the focus and the vertex of a parabola relates to the equation of the parabola. How does changing this distance affect the shape of the parabola?
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