1. Graph quadratic functions.
Find the equation of the axis of symmetry and the coordinates of the vertex of a parabola.
quadratic function
vertex
symmetry
axis of symmetry
parabola
minimum
maximum
Lesson 1 MI/Vocab

2. Key Concept 9-1a

3. Use a table of values to graph y = x2 – x – 2.
Graph Opens Upwards
Use a table of values to graph y = x2 – x – 2.
Graph these ordered pairs and connect them with a smooth curve.
Answer:
Lesson 1 Ex1

4. Use a table of values to graph y = x2 + 2x + 3.
C. D. A B C D
Lesson 1 CYP1

5. Graph these ordered pairs and connect them with a smooth curve.
Graph Opens Downward
A. ARCHERY The equation y = –x2 + 6x + 4 represents the height y of an arrow x seconds after it is shot into the area. Use a table of values to graph y = –x2 + 6x + 4.
Graph these ordered pairs and connect them with a smooth curve.
Answer:
Lesson 1 Ex2

6. Answer: D: {x | x is a real number} R: {y | y ≤ 13}
Graph Opens Downward
B. What are the mathematical domain and range of the function? Describe reasonable domain and range values for this situation.
Answer: D: {x | x is a real number}
R: {y | y ≤ 13}
The arrow is in the air for about 6.6 seconds, so a reasonable domain is D: {x | 0 < x < 6.6}. The height of the arrow ranges from 0 to 13 feet, so a reasonable range is R: {y | 0 < y < 13}.
Lesson 1 Ex2

7. Use a table of values to graph y = –x2 + 4.
C. D. A B C D
Lesson 1 CYP2

8. Key Concept 9-1b

9. Vertex and Axis of Symmetry
A. Consider the graph of y = –2x2 – 8x – 2. Write the equation of the axis of symmetry.
In y = –2x2 – 8x – 2, a = –2 and b = –8.
Equation for the axis of symmetry of a parabola
a = –2 and b = –8
Answer: The equation of the axis of symmetry is x = –2.
Lesson 1 Ex3

10. Vertex and Axis of Symmetry
B. Consider the graph of y = –2x2 – 8x – 2. Find the coordinates of the vertex.
Since the equation of the axis of symmetry is x = –2 and the vertex lies on the axis, the x-coordinate for the vertex is –2.
y = –2x2 – 8x – 2 Original equation
y = –2(–2)2 – 8(–2) – 2 x = –2
y = – – 2 Simplify.
y = 6 Add.
Answer: The vertex is (–2, 6).
Lesson 1 Ex3

11. Vertex and Axis of Symmetry
C. Consider the graph of y = –2x2 – 8x – 2. Identify the vertex as a maximum or minimum.
Answer: Since the coefficient of the x2 term is negative, the parabola opens downward and the vertex is a maximum point.
Lesson 1 Ex3

12. Vertex and Axis of Symmetry
D. Consider the graph of y = –2x2 – 8x – 2. Graph the function.
You can use the symmetry of the parabola to help you draw its graph. On a coordinate plane, graph the vertex and the axis of symmetry.
Choose a value for x other than –2. For example, choose –1 and find the y-coordinate that satisfies the equation.
y = –2x2 – 8x – 2 Original equation
y = –2(–1)2 – 8(–1) – 2 x = –1
y = 4 Simplify.
Lesson 1 Ex3

13. Vertex and Axis of Symmetry
D. Graph the function.
Graph (–1, 4).
Since the graph is symmetrical about its axis of symmetry x = –2, you can find another point on the other side of the axis of symmetry. The point at (–1, 4) is 1 unit to the right of the axis. Go 1 unit to the left of the axis and plot the point (–3, 4).
Lesson 1 Ex3

14. Vertex and Axis of Symmetry
D. Graph the function.
Repeat this for several other points.
Then sketch the parabola.
Lesson 1 Ex3

15. A. Consider the graph of y = 3x2 – 6x + 1
A. Consider the graph of y = 3x2 – 6x + 1. Write the equation of the axis of symmetry.
A. x = –6
B. x = 6
C. x = –1
D. x = 1 A B C D
Lesson 1 CYP3

16. B. Consider the graph of y = 3x2 – 6x + 1
B. Consider the graph of y = 3x2 – 6x + 1. Find the coordinates of the vertex.
A. (–1, 10)
B. (1, –2)
C. (0, 1)
D. (–1, –8) A B C D
Lesson 1 CYP3

17. C. Consider the graph of y = 3x2 – 6x + 1
C. Consider the graph of y = 3x2 – 6x + 1. Identify the vertex as a maximum or minimum.
A. minimum
B. maximum
C. neither
D. cannot be determined A B C D
Lesson 1 CYP3

18. D. Consider the graph of y = 3x2 – 6x + 1. Graph the function.
A. B.
C. D. A B C D
Lesson 1 CYP3

19. Match Equations and Graphs
Which is the graph of y = –x2 – 2x –2?
A B
C D
Lesson 1 Ex4

20. Match Equations and Graphs
Read the Test Item You are given a quadratic function, and you are asked to choose its graph.
Solve the Test Item Find the axis of symmetry of the graph y = –x2 – 2x – 2.
Equation for the axis of symmetry
a = –1 and b = –2
Lesson 1 Ex4

21. Match Equations and Graphs
The axis of symmetry is –1. Look at the graphs. Since only choices C and D have x = –1 as their axis of symmetry, you can eliminate choices A and B. Since the coefficient of the x2 term is negative, the graph opens downward. Eliminate choice C.
Answer: D
Lesson 1 Ex4

22. Which is the graph of y = –x2 + 2x?
A. B.
C. D. A B C D
Lesson 1 CYP4