Parts of a Parabola Worksheet
Explore and identify the key components of a parabola, including the vertex, focus, directrix, and axis of symmetry.
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Parts of a Parabola
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Read each question carefully and provide the best answer. Show all your work where applicable.
1. Define a parabola in your own words, focusing on its geometric definition.
2. What is the relationship between the focus and the directrix of a parabola?
3. The is the turning point of a parabola.
4. The line about which the parabola is symmetric is called the .
5. A parabola is the set of all points that are equidistant from a fixed point (the ) and a fixed line (the ).
6. For a parabola with the equation y = ax² + bx + c, if 'a' is positive, the parabola opens:
Upwards
Downwards
Leftwards
Rightwards
7. The standard form of a parabola that opens vertically is:
(x - h)² = 4p(y - k)
(y - k)² = 4p(x - h)
y = mx + b
y = ax² + bx + c
8. For the parabola with equation (x - 2)² = 8(y + 1), identify the vertex, focus, directrix, and axis of symmetry.
Vertex:
Focus:
Directrix:
Axis of Symmetry:
9. Plot the vertex, focus, and directrix for the parabola (y - 3)² = -12(x + 1). Then sketch the parabola on the graph.