Exploring Quadratic Graphs

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Presentation transcript:

Exploring Quadratic Graphs ALGEBRA 1 LESSON 8-1 Identify the vertex of each graph. Tell whether it is a minimum or a maximum. a. b. The vertex is (1, 2). The vertex is (2, –4). It is a maximum. It is a minimum. 8-1

Exploring Quadratic Graphs ALGEBRA 1 LESSON 8-1 Make a table of values and graph the quadratic function y = x2. 1 3 x y = x2 (x, y) 1 3 0 (0)2 = 0 (0, 0) 2 (2)2 = 1 (2, 1 ) 3 (3)2 = 3 (3, 3) 8-1

Exploring Quadratic Graphs ALGEBRA 1 LESSON 8-1 Use the graphs below. Order the quadratic functions (x) = –x2, (x) = –3x2, and (x) = x2 from widest to narrowest graph. 1 2 (x) = x2 1 2 (x) = –x2 (x) = –3x2 Of the three graphs, (x) = x2 is the widest and (x) = –3x2 is the narrowest. 1 2 So, the order from widest to narrowest is (x) = x2, (x) = –x2, (x) = –3x2. 1 2 8-1

Exploring Quadratic Graphs ALGEBRA 1 LESSON 8-1 Graph the quadratic functions y = 3x2 and y = 3x2 – 2. Compare the graphs. x y = 3x2 y = 3x2 – 2 2 12 10 1 3 1 0 0 2 –1 3 1 The graph of y = 3x2 – 2 has the same shape as the graph of y = 3x2, but it is shifted down 2 units. 8-1

Exploring Quadratic Graphs ALGEBRA 1 LESSON 8-1 A monkey drops an orange from a branch 26 ft above the ground. The force of gravity causes the orange to fall toward Earth. The function h = –16t2 + 26 gives the height of the orange, h, in feet after t seconds. Graph this quadratic function. Use positive values for t. Graph t on the x-axis and h on the y-axis. Height h is dependent on time t. t h = –16t2 + 26 0 26 1 10 2 –38 8-1

Exploring Quadratic Graphs ALGEBRA 1 LESSON 8-1 1. a. Graph y = – x2 – 1. b. Identify the vertex. Tell whether it is a maximum or a minimum. c. Compare this graph to the graph of y = x2. 2. a. Graph y = 4x2 + 3. b. Identify the vertex. Tell whether it is a maximum or a minimum. 1 2 (0, -1); maximum This graph is wider, opens downward, and is shifted one unit down. (0, 3); minimum This graph is narrower and shifted 3 units up. 3. Order the quadratic functions y = –4x2, y = x2, and y = 2x2 from widest to narrowest graph. 1 4 y = x2, y = 2x2, y = –4x2 1 4 8-1