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Parabolas Worksheet
NAME: ______________________________
1) Points A, B, C and P are on the parabola y 
1 2
x  1 , whose focus is F(0, 0) and whose directrix
4
d is the line y = -2. See the graph at right.
a)
b)
c)
d)
e)
f)
Find the distance from A to F and from A to d.
Find the distance from B to F and from B to d.
Find the distance from C to F and from C to d.
Find the distance from P to F and from P to d.
What do you notice about the distances found
in each part above?
What is the relationship between the focus,
any point on the directrix and any point (x, y) on the parabola?
2) In a few sentences, describe how to tell whether a parabola opens up, down, left or right when
you are given an equation.
3) Tell whether the parabola opens up, down, left or right.
a)
b)
1
2
 y  3   x  5 
4
1
2
 x  3   y  5 
4
1
2
 y  3   x  5 
4
1
2
d)   x  3   y  5
4

b)
4) Explain how to use the graph of the equation y  x 2 to graph the equation y  k   x  h  .
2
For each parabola below, give the coordinates of its vertex and focus and give the equation of its
directrix. Sketch graphs as needed to help you.
5)
y
1 2
x
8
9) y  1 
1
2
 x  2
4
12) 4 y  x 2  8x  12
6) x  
1 2
y
12
10) 2  x  4    y  3
7) x  2 y 2
2
13) 2 y 2  8 y  x  3  0
11) y  5  6 x  3x 2
8) y  x 2  1
Parabolas Worksheet
Find an equation of each parabola below. Sketch graphs as needed to help you.
1
)
4
14) Focus, (-1, 0); Directrix, x = 1
15) Vertex (0, 0); Focus, (0, 
16) Focus, (-7, -5); Directrix, y = -7
17) Vertex (1, 3); Focus, (1, 5)
18) Vertex, (-2, -1); Directrix, x = -4
19)Vertex, (0, 6); Directrix, y = 7
1
2
20)Vertex, (1, 0); Point on parabola, (4, 18) and opens up
21) Vertex, (6, 4); Point on parabola, (2, -1) and has a horizontal axis
22) A satellite dish used to receive television signals has a parabolic cross-section as shown below.
Incoming signals that are parallel to the axis of the parabola (aka: axis of symmetry) are reflected to its
focus. Thus, the incoming signal is magnified. Find an equation of the parabola.