Exploring Quadratic Graphs Lesson 10 1 Algebra 1

Exploring Quadratic Graphs Lesson 10 -1 Algebra 1 Additional Examples Identify the vertex of each graph. Tell whether the vertex 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.

Exploring Quadratic Graphs Lesson 10 -1 Algebra 1 Additional Examples Make a table of values and graph the quadratic function y = 1 x 2. 3 x y = 1 x 2 (x, y) 0 1 (0)2 = 0 3 (0, 0) 2 1 (2)2 = 1 1 3 3 3 1 (3)2 = 3 3 3 (2, 1 1 ) 3 (3, 3)

Exploring Quadratic Graphs Lesson 10 -1 Algebra 1 Additional Examples Use the graphs below. Order the quadratic functions 1 (x) = –x 2, (x) = – 3 x 2, and (x) = 2 x 2 from widest to narrowest graph. (x) = –x 2 (x) = – 3 x 2 (x) = 1 x 2 2 Of the three graphs, (x) = 1 x 2 is the widest and (x) = – 3 x 2 is the 2 narrowest. So, the order from widest to narrowest is (x) = 1 x 2, (x) = –x 2, 2 2 (x) = – 3 x.

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

Exploring Quadratic Graphs Lesson 10 -1 Additional Examples Algebra 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 = – 16 t 2 + 26 gives the height of the orange, h, in feet after t seconds. Graph this quadratic function. Height h is dependent on time t. t 0 1 2 h = – 16 t 2 + 26 26 10 – 38 Graph t on the x-axis and h on the y-axis. Use positive values for t.