Parabola Exploration Worksheet
A Grade 10 math worksheet focusing on understanding and analyzing parabolas, including their equations, vertices, foci, and directrices.
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Parabola Exploration Worksheet
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. Which of the following is the standard form equation of a parabola that opens upwards or downwards?
(x - h)² = 4p(y - k)
(y - k)² = 4p(x - h)
Ax + By = C
x² + y² = r²
2. What is the focus of the parabola y² = 12x?
(3, 0)
(-3, 0)
(0, 3)
(0, -3)
3. The set of all points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix) is called a .
4. For a parabola with the equation x² = 4py, the vertex is at the .
5. Find the vertex, focus, and directrix of the parabola (y - 2)² = 8(x + 1). Then sketch the graph on the coordinate plane below.
Vertex:
Focus:
Directrix:
6. The axis of symmetry for a parabola with the equation x = ay² + by + c is a horizontal line.
True
False
7. A parabolic arch has a span of 40 feet and a maximum height of 15 feet. Find the equation of the parabola.