4-1 Study Guide and Intervention Graphing Quadratic Functions Graph Quadratic Functions Quadratic Function A function defined by an equation of the form f(x) = , where a ≠ 0 Graph of a A parabola with these characteristics: y-intercept: c; axis of symmetry: x = ; Quadratic Function x-coordinate of vertex: Example: Find the the equation of the axis of symmetry, and the of the vertex for the y-intercept, x-coordinate graph of = . Use this information to graph the function. f(x) = 1, = and = 5, so the is 5. The equation of the axis of symmetry is = or . The of the a b c y-intercept x x-coordinate –3, vertex is . Next make a table of values for near . x (x, x f(x) f(x)) 0 5 (0, 5) 1 3 (1, 3) 3 3 + 5 – 2 2 3 (2, 3) 3 5 (3, 5) Exercises Complete parts a-c for each quadratic function. a. Find the the equation of the axis of symmetry, and the of the vertex. y-intercept, x-coordinate b. Make a table of values that includes the vertex. c. Use this information to graph the function. 1. = 2. = 3. = f(x) f(x) f(x) 4-1 Study Guide and Intervention (continued) Graphing Quadratic Functions Maximum and Minimum Values The of the vertex of a quadratic function is the maximum value or y-coordinate minimum value of the function. Maximum or Minimum Value The graph of (x) = , where 0, opens up and has a minimum when > 0. The f a a ≠ of a Quadratic Function graph opens down and has a maximum when < 0. a
4-1 Study Guide and Intervention Graphing Quadratic Functions Graph Quadratic Functions Quadratic Function A function defined by an equation of the form f(x) = , where a ≠ 0 Graph of a Quadratic Function A parabola with these characteristics: y-intercept: c; axis of symmetry: x = ; x-coordinate of vertex: Example: Find the y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex for the graph of f(x) = . Use this information to graph the function. a = 1, b = –3, and c = 5, so the y-intercept is 5. The equation of the axis of symmetry is x = or . The x-coordinate of the vertex is . Next make a table of values for x near . x f(x) (x, f(x)) 0 5 (0, 5) 1 3 (1, 3) 3 2 – 3 + 5 2 3 (2, 3) 3 5 (3, 5) Exercises Complete parts a-c for each quadratic function. a. Find the y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex. b. Make a table of values that includes the vertex. c. Use this information to graph the function. 1. f(x) = 2. f(x) = 3. f(x) = 4-1 Study Guide and Intervention (continued) Graphing Quadratic Functions Maximum and Minimum Values The y-coordinate of the vertex of a quadratic function is the maximum value or minimum value of the function. Maximum or Minimum Value of a Quadratic Function The graph of f (x) = , where a ≠ 0, opens up and has a minimum when a > 0. The graph opens down and has a maximum when a < 0.
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