Parts of a Parabola Worksheet
Explore the key features and terminology of parabolas, including vertex, focus, directrix, and axis of symmetry, through various problem types.
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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. A parabola is the set of all points in a plane that are equidistant from a fixed point, called the , and a fixed line, called the .
2. The of a parabola is the point where the parabola changes direction.
3. The is a line that divides the parabola into two symmetrical halves.
4. For a parabola opening upwards or downwards, its axis of symmetry is a line.
5. Which of the following equations represents a parabola that opens to the right?
y = x² + 2x - 3
x = y² - 4y + 1
y = -2x² + 5
x = -3y² + 2y - 7
6. The vertex of the parabola given by y = (x - 3)² + 2 is:
(3, 2)
(-3, 2)
(3, -2)
(-3, -2)
7. For the parabola with equation x² = 12y, identify the coordinates of the focus and the equation of the directrix.
8. Write the equation of a parabola with vertex at (0,0) and directrix y = -4.
9. Consider the parabola defined by the equation y = x² - 6x + 5.
a) Find the vertex of the parabola.
b) Find the equation of the axis of symmetry.
c) Sketch the parabola on the graph below, clearly marking the vertex and axis of symmetry.
Match each term with its definition.
10. Focus
a. The point where the parabola intersects its axis of symmetry.
11. Directrix
b. A fixed point from which all points on the parabola are equidistant.
12. Vertex
c. A fixed line from which all points on the parabola are equidistant.