Translating Parabolas Worksheet - Pretty Math

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Translating Parabolas

Big Idea

Vocabulary

Prerequisite
 coordinate
 line of symmetry
 square
 square root
 parabola
 quadratic
 reflection
 vertex
 x-intercept
New
 intercept form
 maximum value
 minimum value
 vertex form
 translate

. ‫اﻟرﯾﺎﺿﯾﺎت – ﺗﻔﻛﯾر ﺳﻠﯾم – دﻗﺔ وﺗﻌﺎون – ﺻﺑر وﻧظﺎم – ﺗذوق اﻟﺟﻣﺎل اﻟﻌﻠﻣﻲ‬
Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensatioMn

Translating Parabolas

Discovery 4

Translating Parabolas gx = x-12

Example: Graph the equations A. y  x2 3

and B. y  x 12 . How is the graph of fx = x2 2
1
equation A geometrically related to the
graph of equation B? -2 (0,0) (1,0) 2 4

Graph B is translated one unit to the right. 7. Graph the equations A. y  x2 and

6. Graph the equations A. y  x2 and B. y  x2  1. How is the graph of
B. y  x2  1. How is the graph of
equation 7A geometrically related to
equation 6A geometrically related to the graph of equation 7B?
the graph of equation 6B?

. ‫اﻟرﯾﺎﺿﯾﺎت – ﺗﻔﻛﯾر ﺳﻠﯾم – دﻗﺔ وﺗﻌﺎون – ﺻﺑر وﻧظﺎم – ﺗذوق اﻟﺟﻣﺎل اﻟﻌﻠﻣﻲ‬
Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensatioMn

Translating Parabolas

8. Graph the equations A. y  x2 and 9. Graph the equations A. y  x2 and
B. y  2x . How is the graph of
B. y  1 x . How is the graph of
equation 8A geometrically related to 2
the graph of equation 8B? equation 9A geometrically related to

the graph of equation 9B?

10. Graph the equations A. y  2x2 and 11. Graph the equations A. y  x2 and

B. y  2(x 1)2 . How is the graph of B. y  x2 . How is the graph of

equation 10A geometrically related to equation 11A geometrically related to
the graph of equation 10B? the graph of equation 11B?

. ‫اﻟرﯾﺎﺿﯾﺎت – ﺗﻔﻛﯾر ﺳﻠﯾم – دﻗﺔ وﺗﻌﺎون – ﺻﺑر وﻧظﺎم – ﺗذوق اﻟﺟﻣﺎل اﻟﻌﻠﻣﻲ‬
Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensatioMn

Translating Parabolas

12.Graph the equations A. y  x2 and 13.Graph the equations A. y  2(x  1)2

y  x 12 . How is the graph of and y  2x2  1. How is the graph if

equation 6A geometrically related to equation 13A geometrically related to
the graph of equation 6B? the graph of 13 B?

Predict what the graphs of each of the following equations will look like by
sketching it. Then use a graphing calculator to verify your graph.

14. y  x2  2 15. y  3x2

. ‫اﻟرﯾﺎﺿﯾﺎت – ﺗﻔﻛﯾر ﺳﻠﯾم – دﻗﺔ وﺗﻌﺎون – ﺻﺑر وﻧظﺎم – ﺗذوق اﻟﺟﻣﺎل اﻟﻌﻠﻣﻲ‬
Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensatioMn

16. y  1 x  12 Translating Parabolas
3
17. y  3x  1

18. y  2x  22  2 19. y  x 1 1

. ‫اﻟرﯾﺎﺿﯾﺎت – ﺗﻔﻛﯾر ﺳﻠﯾم – دﻗﺔ وﺗﻌﺎون – ﺻﺑر وﻧظﺎم – ﺗذوق اﻟﺟﻣﺎل اﻟﻌﻠﻣﻲ‬
Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensatioMn

Translating Parabolas

Vertex Form of a Quadratic Equation

Vertex

The vertex of a parabola
is the point where the
parabola reaches a
maximum (for parabolas
that opens downwards),
or a minimum (for
parabolas that open
upwards).

Line of Symmetry

For every parabola, a
line can be drawn
through the vertex that
is equidistant from
corresponding parts of
the parabola. Look figure

1. Line segment A goes from the parabola to the line of symmetry. Line segment A'
goes from the line of symmetry to the opposite side of the parabola. Line A and A'

are the same length.

20. If we reflect the parabola around its line of symmetry, what will we get?

____________________________________________

21. The vertex of a parabola is at the _______________ or _________________ of the

parabola. 2

22. If the length of the line segment A in Figure 2

figure 2 is 14, what is the length of line
segment B ?
1

23. What is the vertex of the parabola in figure A B
2?
-2 -1
24. Does the parabola in figure 2 open upwards
or downwards?

. ‫اﻟرﯾﺎﺿﯾﺎت – ﺗﻔﻛﯾر ﺳﻠﯾم – دﻗﺔ وﺗﻌﺎون – ﺻﺑر وﻧظﺎم – ﺗذوق اﻟﺟﻣﺎل اﻟﻌﻠﻣﻲ‬
Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensatioMn

Translating Parabolas
Describe the effect that each change has on the graph of each original
equation.

Example: changing y  3(x 1)2  2 to y  3(x 1)2 1.
Changing y  3(x 1)2  2 to y  3(x 1)2 1 translates the parabola down 3.
25.changing y  3(x  1)2  1 to y  3(x  2)2  1
26.changing y  3(x 1)2  1 to y  6(x 1)2  1
27.changing y  1(x  1)2  1 to y  1(x 1)2 1
28.changing y  1(x 1)2  2 to y  1(x  2)2  1

Complete the following.

 29.When a quadratic equation is in the form y  a(x  h)  k , the point h, k is

the _______________ of the parabola.

The form y  a(x  h)  k is called the vertex form of a quadratic equation. This is

because the point (h, k) is the vertex of the parabola.

. ‫اﻟرﯾﺎﺿﯾﺎت – ﺗﻔﻛﯾر ﺳﻠﯾم – دﻗﺔ وﺗﻌﺎون – ﺻﺑر وﻧظﺎم – ﺗذوق اﻟﺟﻣﺎل اﻟﻌﻠﻣﻲ‬
Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensatioMn

Translating Parabolas

Give the equation of the following parabolas in vertex form.
8 30.

8

6
6

4
4

2
2

-5 (0,0) 5 (1,1) 5
-5 5
-2 -2

Example: y  (x  0)2  0

31. 8 32. 6
6 4
-5 4 -5 2
2 5
-2
(-2,1)
(-1,-2)
-2

. ‫اﻟرﯾﺎﺿﯾﺎت – ﺗﻔﻛﯾر ﺳﻠﯾم – دﻗﺔ وﺗﻌﺎون – ﺻﺑر وﻧظﺎم – ﺗذوق اﻟﺟﻣﺎل اﻟﻌﻠﻣﻲ‬
Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensatioMn

Translating Parabolas

Give the equation of the following parabolas in vertex form.

Example:

8

Step 1: Write down y  a(x  h)2  k
the general vertex
6 form of a quadratic
equation.

4 Step 2: Substitute the y  a(x 1)2 1

(0,3) vertex for h and k .

2

(1,1) Step 3: Substitute the 3  a(0 1) 21

other point for x and
y.
-5 5

Step 4: Solve for a . 3  a(1)2  1

3  a(1) 1

3  a 1
31 a 11
2a

Step 5 Rewrite the y  2(x 1) 1
equation.

. ‫اﻟرﯾﺎﺿﯾﺎت – ﺗﻔﻛﯾر ﺳﻠﯾم – دﻗﺔ وﺗﻌﺎون – ﺻﺑر وﻧظﺎم – ﺗذوق اﻟﺟﻣﺎل اﻟﻌﻠﻣﻲ‬
Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensatioMn

Translating Parabolas

33. 34.

2 6
4
(2,1)
(2,2)
-2 5
-5 2
(0,-3)
(-1,-1)
-4
-2
-6

35. 36. 8

6 5 6
-5
(1,5) 4

4 2
2
(0,1)
-2 (-1,1/3)

(-1,-3)

. ‫اﻟرﯾﺎﺿﯾﺎت – ﺗﻔﻛﯾر ﺳﻠﯾم – دﻗﺔ وﺗﻌﺎون – ﺻﺑر وﻧظﺎم – ﺗذوق اﻟﺟﻣﺎل اﻟﻌﻠﻣﻲ‬
Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensatioMn