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1. Determine the equation of the parabola 2xy after each of the
following transformations: (Write eachequation in standard and
general form Do each part separately)
(a) Translation 3 units down (b) Shift 5 units right(c)
Horizontal stretch by a factor of 4, shifted 1 unit up(d) Vertical
stretch by a factor of
9
1, shifted 3 units right
2. Convert to standard form (if necessary) to graph and state
the:i Coordinates of Vertex ii Direction of opening
iii Domain and Range iv Stretch Factor
(a)2)5(32 xy (b)
2)5(
4
11 yx
(c)2
42 yx (d)2)7(62 xy
(e) 01462
yxx (f) 022
xy
(g) 0322
yxy (h) 0974042
yxx
(i) 0681642
yxy (j) 0151222
yxx
e
3.
Given the following graphs, write the equation, in standard and
general form, that gives the parabola:
x- 6 - 4 - 2 2 4 6
y
- 4
- 2
2
4
6
8
10
x- 6 - 4 - 2 2 4 6
y
- 6
- 4
- 2
2
4
6
x- 10 - 8 - 6 - 4 - 2 2
y
- 8
- 6
- 4
- 2
2
4
x- 6 - 4 - 2 2 4
y
- 6
- 4
- 2
2
4
x- 10 - 8 - 6 - 4 - 2 2 4 6
y
- 5
5
10
x- 8 - 6 - 4 - 2 2 4 6 8 10 12
y
- 6
- 4
- 2
2
4
6
8
(a) (b) (c)
(d) (e) (f)
Do work on Separate Paper!
8/2/2019 Conics 5 Parabolas
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4. A parabola given by the equation 2x y has the following
transformations applied: A horizontal stretch by a factorof 4,
shifted 3 units to the right and 1 unit down. State the standard
and general form equation of the transformed
parabola.
5. A parabola given by the equation 2y x has the following
transformations applied: A vertical stretch by a factor of1/3,
shifted 5 units to the left and 2 units down. State the standard
and general form equation of the transformed
parabola.
6. A parabola given by the equation 2y x has the following
transformations applied: A horizontal stretch by a factorof 1/5,
reflected about the line y=0, shifted 1 unit to the right. State
the standard and general form equation of the
transformed parabola.
7. A parabola with an equation 23 ( 2)x y is horizontally
stretched by a factor of 3 about the line 2x . Statethe new
standard and general form equation.
8. A parabola with an equation 2( 1) 2y x is vertically
stretched by a factor of 2 about the line 4y . Statethe new
standard and general form equation.
9. Given a parabola with an equation 24 2( 1)y x , algebraically
determine any x, y intercepts. (Nearesthundredth if necessary)
10. Given a parabola with an equation 2 4 6 1 0y x y , convert
to standard form and algebraically determine anyx, y intercepts.
(Nearest hundredth if necessary)
1. (a) 2 3y x (b) 2( 5)y x (c) 21
116
y x (d)21 ( 3)
9y x
2. (a) (i) (-5, -2) (ii) Down (iii) : { }D , : { 2}R y (iv) 3
vert. (b) (i) (1, -5) (ii) Right (iii) : { 1}D x , : { }R (iv)
horiz.
(c) (i) (-2, 0) (ii) Right (iii) : { 2}D x , : { }R (iv) horiz.
(d) (i) (-7, 3) (ii) Up (iii) : { }D , : { 3}R y (iv) vert.
(e) (i) (3, 5) (ii) Up (iii) : { }D , : { 5}R y (iv) 1 vert. (f)
(i) (0, 0) (ii) Left (iii) : { 0}D x , : { }R (iv) 2 horiz.
(g) (i) (-2, 1) (ii) Left (iii) : { 2}D x , : { }R (iv) 1 horiz.
(h) (i) (-5, 3) (ii) Down (iii) : { }D , : { 3}R y (iv) 4 vert.
(i) (i) (1, 8) (ii) Right (iii) : { 1}D x , : { }R (iv) horiz.
(j) (i) (-3, 3) (ii) Down (iii) : { }D , : { 3}R y (iv) 2 vert.
3. General Form only are provided.(a) 23 12 4 8 0x x y (b) 2 2 6
0y x (c) 22 4 6 0y x y (d) 23 12 2 6 0x x y
(e) 2 8 3 10 0x x y (f) 27 9 28 73 0y x y
4. 23 4( 1)x y , 24 8 7 0y x y 5. 22 1 /3( 5)y x , 2 10 3 19 0x
x y
6. 225( 1)y x , 225 50 25 0x x y 7. 25 3( 2)x y , 23 12 17 0y x
y
8. 22( 1)y x , 22 4 2 0x x y 9. 0.41, -2.41 2x y 10. 0.25 0.17,
5.83x y
