1. Completely labeled graph
Assignment, red pen, highlighter, textbook, GP notebook, graphing calculator
U4D1
Have out:
Bellwork:
Graph y = (x + 3)2 for –6 ≤x ≤0. Be sure to label your graph completely. y x 2 4 6 –2 –4 –6 8 10 x y –6 –5 –4 –3 –2 –1 9 +3 4
y = (x + 3)2 +1
parabola 1 +1 1
Completely labeled graph 4 9
Vertex
(–3, 0)
total:

2. Take out the Translate Parabolas worksheet
Part 1: Graph the parabolas using a graphing calculator. Record any observations you notice about the similarities and differences of each parabola with the parent graph, y = x2. x y 4 6 8 10 2 –2 –4 –6 –8
–10
Parent Graph: y = x2 x -3 -2 -1 1 2 3 y 9 4 1 1 4 9

3. The graph is shifted right 7 units.
Parent Graph: y = x2
y = (x – 7)2 x y 4 6 8 10 2 –2 –4 –6 –8
–10 x y 4 6 8 10 2 –2 –4 –6 –8
–10
Observations:
The graph is shifted right 7 units.

4. The graph is shifted left 2 units. The graph is shifted right 3 units.
y = (x + 2)2
y = (x – 3)2 x y 4 6 8 10 2 –2 –4 –6 –8
–10 x y 4 6 8 10 2 –2 –4 –6 –8
–10
The graph is shifted left 2 units.
The graph is shifted right 3 units.

5. Conclusions: y = a(x – h)2 + k x + h left x – h right
The general equation of parabolas is _________________.
Describe what h does to the equation:
x + h
left
______ shifts the graph to the ________.
x – h
right
______ shifts the graph to the ________.

6. WITHOUT using a graphing calculator, graph the following parabolas using the patterns you previous discovered. Be sure to identify the vertex.
Practice #1:
a) y = (x – 4)2
b) y = (x + 6)2
Shift the parent graph ___ units ______. Vertex: ________ 4
Shift the parent graph ___ units ______. Vertex: ________ 6
right
(4, 0)
left
(–6, 0) x y 4 6 8 10 2 –2 –4 –6 –8
–10 x y 4 6 8 10 2 –2 –4 –6 –8
–10

7. WITHOUT using a graphing calculator, graph the following parabolas using the patterns you previous discovered. Be sure to identify the vertex.
Practice:
c) y = (x + 1)2
d) y = (x – 8)2
Shift the parent graph ___ units ______. Vertex: ________ 1
Shift the parent graph ___ units ______. Vertex: ________ 8
left
(–1, 0)
right
(8, 0) x y 4 6 8 10 2 –2 –4 –6 –8
–10 x y 4 6 8 10 2 –2 –4 –6 –8
–10

8. The graph is shifted up 5 units. The graph is shifted down 9 units.
Part 2: Graph the parabolas using a graphing calculator. Record any observations you notice about the similarities and differences of each parabola with the parent graph, y = x2.
y = x2 + 5
y = x2 – 9
The graph is shifted up 5 units.
The graph is shifted down 9 units. x y 4 6 8 10 2 –2 –4 –6 –8
–10 x y 4 6 8 10 2 –2 –4 –6 –8
–10

9. The graph is shifted down 2 units.
Part 2: Graph the parabolas using a graphing calculator. Record any observations you notice about the similarities and differences of each parabola with the parent graph, y = x2.
y = x2 – 2
y = (x – 4)2 + 3
The graph is shifted down 2 units.
The graph is shifted right 4 units and up 3 units. x y 4 6 8 10 2 –2 –4 –6 –8
–10 x y 4 6 8 10 2 –2 –4 –6 –8
–10

10. Conclusions: + k up – k down y = a(x – h)2 + k
Given that the general equation of parabolas is y = a(x – h)2 + k, describe what k does to the equation:
+ k up
______ shifts the graph ________.
– k
down
______ shifts the graph ________.
Put it together:
y = a(x – h)2 + k
Shifts the parabola up or down
Shifts the parabola left or right

11. Practice #2: a) y = x2 – 4 b) y = (x + 7)2 0 units left 7 units
WITHOUT using a graphing calculator, graph the following parabolas. Identify the types of translation and the vertex.
Practice #2:
a) y = x2 – 4
b) y = (x + 7)2
0 units
left 7 units
Horizontal Shift: ___________
Horizontal Shift: ___________
down 4 units
0 units
Vertical Shift: _____________
Vertical Shift: _____________
(0, –4)
(–7, 0)
Vertex: _______
Vertex: _______ x y 4 6 8 10 2 –2 –4 –6 –8
–10 x y 4 6 8 10 2 –2 –4 –6 –8
–10

12. Practice #2: c) y = (x – 1)2 – 9 d) y = (x + 2)2 – 3 right 1 units
WITHOUT using a graphing calculator, graph the following parabolas. Identify the types of translation and the vertex.
Practice #2:
c) y = (x – 1)2 – 9
d) y = (x + 2)2 – 3
right 1 units
left 2 units
Horizontal Shift: ___________
Horizontal Shift: ___________
down 9 units
down 3 units
Vertical Shift: _____________
Vertical Shift: _____________
(1, –9)
(–2, –3)
Vertex: _______
Vertex: _______ x y 4 6 8 10 2 –2 –4 –6 –8
–10 x y 4 6 8 10 2 –2 –4 –6 –8
–10

13. Finish today's assignment:
worksheet & PG

14. OLD SLIDES

15. Let's look at PG - 5
from yesterday's
assignment.

16. Investigate a Parabola
PG – 5
Investigate a Parabola
a) Draw the graph of y = (x – 2)2. Since we are going to do this by hand, be sure to use the domain –1 ≤ x ≤ 5. y x 2 4 6 –2 –4 –6 8 10 x y –1 1 2 3 4 5 9 4 1
y = (x – 2)2 1 4 9
Vertex
(2, 0)

17. Investigate a Parabola
PG – 5
Investigate a Parabola
b) How is this graph different from the graph of y = x2? What difference in the equation accounts for the difference in graphs? y x 2 4 6 –2 –4 –6 8 10 x
y = x2 –3 –2 –1 1 2 3
The graph of y = (x – 2)2 is shifted 2 units to the right. 9
y = x2 4 1
The “2” makes the graph shift over. 1
y = (x – 2)2 4 9

18. Investigate a Parabola
PG – 5
Investigate a Parabola
b) Based on your observations in part (b), write an equation with a graph that “sits on” the x–axis at the point (5, 0). y x 2 4 6 –2 –4 –6 8 10
y = (x – 5)2
y = x2
y = (x – 2)2