NAME _____________________________________________ DATE ____________________________ PERIOD _____________
8.5 Parabolas-General Form to Standard Form
Identify the vertex, focus, axis of symmetry, and directrix for each equation. Then graph the parabola.
𝑥−1 2
)
4
1. (
𝑦–2
)
2
= (
Write an equation for and graph a parabola with the given characteristics.
2. vertex (–2, 4) , focus (–2, 3)
3. Write 𝑥 2 + 8x = –4y – 8 in standard form.
4. SATELLITE DISH Suppose the receiver in a parabolic dish antenna is 2 feet from the vertex and is located at the
focus. Assume that the vertex is at the origin and that the dish is pointed upward. Find an equation that models a cross
section of the dish.
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
5. Write the following parabolas in standard form. Then identify the focus, axis of symmetry, and directrix for
each equation
a. x 2  17  8 y  39
b. y 2  33  8x  23
c. 12 y  10  x 2  4 x  14
d. y 2  6 y  21  20 x  68
e. 2 y 2  16 y  72  20 x
f. 2 x2  20 x  8 y  34
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
8.5 Parabolas-General Form to Standard Form
Identify the vertex, focus, axis of symmetry, and directrix for each equation. Then graph the parabola.
𝑥−1 2
)
4
1. (
𝑦–2
)
2
= (
Solution:
Write an equation for and graph a parabola with the given characteristics.
2. vertex (–2, 4) , focus (–2, 3)
Solution:
3. Write 𝑥 2 + 8x = –4y – 8 in standard form.
Solution:
4. SATELLITE DISH Suppose the receiver in a parabolic dish antenna is 2 feet from the vertex and is located at the
focus. Assume that the vertex is at the origin and that the dish is pointed upward. Find an equation that models a cross
section of the dish.
Solution: x 2  8 y
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
5. Write the following parabolas in standard form. Then identify the focus, axis of symmetry, and directrix for
each equation
a. x 2  17  8 y  39
x 2  8( y  7)
Solution:
Vertex: (0,-7)
Focus: (0,-5)
Directrix: y=-9
Axis of symmetry: x=0
b. y 2  33  8x  23
y 2  8( x  7)
Solution:
Vertex: (-7,0)
Focus: (-9,0)
Directrix: x=-5
Axis of symmetry: y=0
c. 12 y  10  x 2  4 x  14
Solution:
( x  2)2  12 y
Vertex: (2,0)
Focus: (2,-3)
Directrix: y=3
Axis of symmetry: x=2
d. y 2  6 y  21  20 x  68
Solution:
( y  3)2  20( x  4)
Vertex: (-4,-3)
Focus: (-9,-3)
Directrix: x=1
Axis of symmetry: y=-3
e. 2 y 2  16 y  72  20 x
Solution:
( y  4)2  10( x  2)
Vertex: (2,4)
Focus: (4.5,4)
Directrix: x=-0.5
Axis of symmetry: y=4
f. 2 x2  20 x  8 y  34
Solution:
( x  5)2  4( y  2)
Vertex: (-5,2)
Focus: (-5,1)
Directrix: y=3
Axis of symmetry: x=-5