9 4 Transforming Quadratic Functions Objective Graph and

9 -4 Transforming Quadratic Functions Objective Graph and transform quadratic functions. Holt Mc. Dougal Algebra 1

9 -4 Transforming Quadratic Functions The quadratic parent function is f(x) = x 2. The graph of all other quadratic functions are transformations of the graph of f(x) = x 2. For the parent function f(x) = x 2: • The axis of symmetry is x = 0, or the y-axis. • The vertex is (0, 0) • The function has only one zero, 0. Holt Mc. Dougal Algebra 1

9 -4 Transforming Quadratic Functions Holt Mc. Dougal Algebra 1

9 -4 Transforming Quadratic Functions The value of a in a quadratic function determines not only the direction a parabola opens, but also the width of the parabola. Holt Mc. Dougal Algebra 1

9 -4 Transforming Quadratic Functions Example 1 Order the functions from narrowest graph to widest. f(x) = 3 x 2, g(x) = 0. 5 x 2 Holt Mc. Dougal Algebra 1

9 -4 Transforming Quadratic Functions Example 2 Order the functions from narrowest graph to widest. f(x) = x 2, g(x) = x 2, h(x) = – 2 x 2 Holt Mc. Dougal Algebra 1

9 -4 Transforming Quadratic Functions Example 3 Order the functions from narrowest graph to widest. f(x) = –x 2, g(x) = x 2 Holt Mc. Dougal Algebra 1

9 -4 Transforming Quadratic Functions Holt Mc. Dougal Algebra 1

9 -4 Transforming Quadratic Functions The value of c makes these graphs look different. The value of c in a quadratic function determines not only the value of the y-intercept but also a vertical translation of the graph of f(x) = ax 2 up or down the y-axis. Holt Mc. Dougal Algebra 1

9 -4 Transforming Quadratic Functions Helpful Hint When comparing graphs, it is helpful to draw them on the same coordinate plane. Holt Mc. Dougal Algebra 1

9 -4 Transforming Quadratic Functions Example 4 Compare the graph of the function with the graph of f(x) = x 2. g(x) = x 2 + 3 Holt Mc. Dougal Algebra 1

9 -4 Transforming Quadratic Functions Example 5 Compare the graph of the function with the graph of f(x) = x 2 g(x) = 3 x 2 Holt Mc. Dougal Algebra 1

9 -4 Transforming Quadratic Functions Holt Mc. Dougal Algebra 1

9 -4 Transforming Quadratic Functions The quadratic function h(t) = – 16 t 2 + c can be used to approximate the height h in feet above the ground of a falling object t seconds after it is dropped from a height of c feet. This model is used only to approximate the height of falling objects because it does not account for air resistance, wind, and other real-world factors. Holt Mc. Dougal Algebra 1

9 -4 Transforming Quadratic Functions Example 3: Application Two identical softballs are dropped. The first is dropped from a height of 400 feet and the second is dropped from a height of 324 feet. a. Write the two height functions and compare their graphs. Holt Mc. Dougal Algebra 1