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Graphing Quadratics Using the TI-83

Teacher’s Notes:

Solutions to Developmental Activity:

1.

Equation of parabola Vertex x- intercept (s) y-intercept Axis of symmetry
y = x2 (0, 0) (0, 0) (0, 0) x = 0
y = x2 + 2 (0, 2) None (0, 2) x = 0
y = x2 – 2 (0, -2) 1.41 and –1.41 (0, -2) x = 0
y = x2 + x (-.5, -.25) 0 and –1 (0, 0) x = -.5
y = x2 + 5x (-2.5, -6.25) 0 and –5 (0, 0) x = -2.5
y = x2 – 5x (2.5, -6.25) 5 and 0 (0, 0) x = 2.5
y = x2 – 3x +2 (1.5, -.25) 2 and 1 (0, 2) x = 1.5
y = x2 – 4x (-2,-4) 0 and –4 (0, 0) x = -2
y = x2 – 3x – 4 (1.5, -6.25) 4 and –1 (0, -4) x = 1.5

2. Answers will vary.

3.
a: Changing a will make the parabola more narrow or wide. Changing the sign of a
will make the graph open up or down.
b: Changing b will move the vertex of the parabola .
c: Changing c will change the y-intercept.

Ticket Out:

Answers will be collected as the students exit the room. The information will be used to
assess the students understanding of the lesson covered.

Solutions to Homework:

5. True

7b.

7c. (1, -4); minimum

7d. –3

9a. (-3,1)

9b. x = -3

12a. (-4, 35)

12b. x = -4

12c. 19, 5, -13

Exploring y = ax2 + bx + c

Name: ____________________

Period: _____

Directions: Log on to the computer and go to the following website:

Set the graph tool so that a = 1, b = 0, and c = 0. Click in the box that says show
vertex/ intercept data .

1. Complete the table below:

Equation of parabola Vertex x-intercept y-intercept Axis of symmetry
y = x2        
y = x2 + 2        
y = x2 – 2        
y = x2 + x        
y = x2 + 5x        
y = x2 – 5x        
y = x2 – 3x +2        
  (-2,-4) 0 and –4 (0, 0)  
  (1.5, -6.25) 4 and –1 (0, -4)  

2. Was it difficult to graph the parabola given only the vertex and the intercepts?

3. For each letter a, b, and c give a general rule for what happens when you change only
that value.

a:
b:
c:

Day 3

Lesson Plan:

Objectives:


1. Students will be able to graph and interpret equations of the form y = ax2 + bx + c.

Standards:


• NCTM Standards covered: Algebra , Representation
• NYS Standards covered: 7A, 7C

Materials:

Graphing calculators
• Lesson Master 9-3B and overhead transparency of worksheet
• Overhead with calculator unit

Opening Activity:

The students will answer the following questions upon entering the room.
Tell what you know about a, b, or c in the equation y = ax2 + bx + c if
1. its vertex is its minimum point
2. the y-axis is the axis of symmetry of the graph
3. The point (0, 6) is on the graph.

Developmental Activity:

The students will work with a partner to complete Lesson Master 9-3B. The students will
then be selected to present their answers to the class using the overhead calculator and the
board.

Ticket Out:

Students will have the last 5 minutes of class to respond to the following question, also to
address any concerns they had with the lesson.

When graphing on a TI-83 how important is it to select the correct window size?

Homework:

Read pgs. 562 – 564, complete pg. 565 # 7 –10.

Teacher’s Notes:

Solutions to Opening Activity:


1. The value of a must be greater than 0.

2. b = 0

3. c = 6

Solutions to Developmental Activity:

1.
a. 5
b. –4
c. x = 5

2a.

2b. They will all open down and have the y-axis as their axis of symmetry. Their
vertices are at different points , and their graphs appear to get narrower.

2c. It opens down and has the y-axis as its axis of symmetry. The vertex is at (0, -10). It
is quite narrow.

6
a. (-10, -144)
b. x = -10
c. –14.7 and –5.3

7b. (-1, 2), (3, 10)

Solutions to Homework:



9a.

9b. (-9, -12)

9c. x = -9

9d. –12 and –7

10a. 3

10b. 16


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