1. Algebra 2 Step 1:Graph the vertex, which is the y-intercept (0, 1). Step 2:Make a table of values to find some points on one side of the axis of symmetry x = 0. Graph the points. xyxy 2222 3434 4646 1 1313 1313 1313 1 Step 3:Graph corresponding points on the other side of the axis of symmetry. Graph y = x 2 + 1. Lesson 5-2 Properties of Parabolas 1313 Step 4:Sketch the curve. Additional Examples

2. Algebra 2 Graph y = x 2 + x + 3. Name the vertex and axis of symmetry. Lesson 5-2 Properties of Parabolas 1212 Step 3:Find and graph the y-intercept and its reflection. Since c = 3, the y-intercept is (0, 3) and its reflection is (–2, 3). Step 1:Find and graph the axis of symmetry. x = – = – = –1 b 2a 1 2( ) 1212 Step 2:Find and graph the vertex. The x- coordinate of the vertex is –1. The y-coordinate is y = (–1) 2 + (–1) + 3 = 2. So the vertex is (–1, 2 ). 1212 1212 1212 Additional Examples

3. Algebra 2 Step 4:Evaluate the function for another value of x, such as y = (2) 2 + (2) + 3 = 7. Graph (2, 7) and its reflection (–4, 7). 1212 (continued) Lesson 5-2 Properties of Parabolas Step 5:Sketch the curve. Additional Examples

4. Algebra 2 Graph the vertex and the axis of symmetry x = 4. Graph two points on one side of the axis of symmetry, such as (6, 0) and (8, –3). Then graph corresponding points (2, 0) and (0, –3). The maximum value of the function is 1. Graph y = – x 2 + 2x – 3. What is the maximum value of the function? Since a < 0, the graph of the function opens down, and the vertex represents the maximum value. Find the coordinates of the vertex. Lesson 5-2 Properties of Parabolas x = – = – = 4Find the x-coordinate of the vertex. b 2a 2 2(– ) 1414 y = – (4) 2 + 2(4) – 3 = 1Find the y-coordinate of the vertex. 1414 1414 Additional Examples

5. Algebra 2 Define:Line R = revenue. Let p = price of a get-away package. Let –0.12p + 60 = number of a get-away packages sold. Write:R = p ( –0.12p + 60 ) = –0.12p 2 + 60pWrite in standard form. Relate:revenue equals price times number of get-away packages sold The number of weekend get-away packages a hotel can sell is modeled by –0.12p + 60, where p is the price of a get-away package. What price will maximize revenue? What is the maximum revenue? Lesson 5-2 Properties of Parabolas Additional Examples

6. Algebra 2 Find the maximum value of the function. Since a < 0, the graph of the function opens down, and the vertex represents a maximum value. (continued) Lesson 5-2 Properties of Parabolas R = –0.12(250) 2 + 60(250)Evaluate R for p = 250 = 7500Simplify. A price of $250 will maximize revenue. The maximum revenue is $7500. p = – = – = 250Find p at the vertex. b2a b2a 60 2(–0.12) Additional Examples