Characteristics of Parabolas Worksheet
Explore and identify the key characteristics of parabolas, including vertex, focus, directrix, and axis of symmetry.
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Characteristics of Parabolas
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Read each question carefully and provide the most accurate answer. Show all your work for full credit.
1. For the parabola with equation (x - 3)² = 8(y + 1), identify the following characteristics:
a) Vertex:
b) Focus:
c) Directrix:
d) Axis of Symmetry:
2. Which of the following equations represents a parabola that opens downwards?
y = 2x² + 3x - 1
x = -y² + 5y + 2
y = -x² - 4x + 7
x = 3y² - y + 1
3. The is a fixed point not on the parabola, and the is a fixed line not intersecting the parabola.
4. The distance from any point on a parabola to the focus is equal to its distance to the .
5. Consider the parabola given by the equation y² + 4y + 8x - 4 = 0.
a) Rewrite the equation in standard form.
b) Find the vertex, focus, and directrix.
c) Sketch the graph of the parabola on the coordinate plane below, labeling the vertex, focus, and directrix.
6. All parabolas have a vertical axis of symmetry.
True
False
7. The latus rectum of a parabola is a line segment through the focus, perpendicular to the axis of symmetry, with endpoints on the parabola.
True
False
8. Derive the equation of a parabola with its vertex at the origin (0,0) and its focus at (0, p).