# 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 = x^{2} |
(0, 0) | (0, 0) | (0, 0) | x = 0 |

y = x^{2} + 2 |
(0, 2) | None | (0, 2) | x = 0 |

y = x^{2} – 2 |
(0, -2) | 1.41 and –1.41 | (0, -2) | x = 0 |

y = x^{2} + x |
(-.5, -.25) | 0 and –1 | (0, 0) | x = -.5 |

y = x^{2} + 5x |
(-2.5, -6.25) | 0 and –5 | (0, 0) | x = -2.5 |

y = x^{2} – 5x |
(2.5, -6.25) | 5 and 0 | (0, 0) | x = 2.5 |

y = x^{2} – 3x +2 |
(1.5, -.25) | 2 and 1 | (0, 2) | x = 1.5 |

y = x^{2} – 4x |
(-2,-4) | 0 and –4 | (0, 0) | x = -2 |

y = x^{2} – 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 = ax ^{2} + 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 = x^{2} |
||||

y = x^{2} + 2 |
||||

y = x^{2} – 2 |
||||

y = x^{2} + x |
||||

y = x^{2} + 5x |
||||

y = x^{2} – 5x |
||||

y = x^{2} – 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 = ax

^{2}+ bx + c.

Standards:

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 = ax

^{2}+ 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

Prev | Next |