Parabola Worksheet - GEOMETRY
Parabola Worksheet Name:
Period:
Date:
1. [pic]
opens: p =
vertex focus
directrix axis of symmetry
2. [pic] 3. [pic]
opens: opens:
p = p =
vertex vertex
focus focus
directrix directrix
axis of symmetry axis of symmetry
Rewrite each equation in standard form
4. [pic] 5. [pic]
opens: opens:
p = p =
vertex vertex
focus focus
directrix directrix
axis of symmetry axis of symmetry
Write the equation of each parabola with the given information
6. vertex (-1, 2), focus (-1, 0) 7. directrix y = 8, focus (0,0)
8. vertex (5, 2), focus (3, 2) 9. directrix x = 1, vertex (-2, 1)
Find an equation of the tangent line to the parabola at the given point, and find the x-intercept of the line.
10. [pic] 11. [pic]
12. The revenue R (in dollars) generated by the sale of s units of a digital camera is given by [pic]. Use a graphing utility to graph the function and approximate the number of sales that will maximize revenue.
13. Satellite Antenna The receiver in a parabolic television dish antenna is 4.5 feet from the vertex and is located at the foucs. Write an equation for a cross section of the relector. Assume that the dish is directed upward and the vertes is at the origin.
14. Roads are often designed with parabolic surfaces to allow rain to drain off. A particular road that is 32 feet wide is 0.4 foot higher in the center than it is on the sides. Find an equation of the parabola that models the road surface. How far from the center of the road is the road surface 0.1 foot lower than in the middle?
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