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

Key Concept 9-1a

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

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

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

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

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

Key Concept 9-1b

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

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 = –8 + 16 – 2 Simplify. y = 6 Add. Answer: The vertex is (–2, 6). Lesson 1 Ex3

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

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

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

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

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

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

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

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

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

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

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

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