• Slides: 9

Quadratic Functions Objectives: Graph a Quadratic Function using Transformations Identify the Vertex and Axis of Symmetry of a Quadratic Function Graph a Quadratic Function using its Vertex, Axis and Intercepts

Quadratic Function A function that is defined by a 2 nd degree polynomial in one variable. The domain is Standard form shows the vertex, the axis of symmetry and whether it opens up or down.

Graphing Quadratic Function with Equations in Standard form 1. Determine whether the parabola opens upward or downward 2. Determine the vertex of the parabola 3. Find the x-intercepts by solving 4. Find the y-intercept by computing 5. Plot the intercepts, the vertex, and additional points as necessary. Connect these points with a smooth curve that is shaped like a cup.

Graph the quadratic function 1. 2.

Graphing Quadratic Function with Equations in the form 1. Determine whether the parabola opens upward or downward 2. Determine the vertex of the parabola 3. Find the axis of symmetry 4. Find the y-intercept 5. Plot the vertex, the axis of symmetry, y-intercept and its symmetry point. Connect these points with a smooth curve that is shaped like a cup. and the x-intercepts

Graph each quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, yintercept, and x-intercepts (if any). Determine the domain and the range of the function. Determine where the function is increasing and decreasing. 3.

Graph each quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, yintercept, and x-intercepts (if any). Determine the domain and the range of the function. Determine where the function is increasing and decreasing. • 4.

Determine the quadratic function whose graph is given. 5.

Minimum and Maximum of Quadratic Functions If , then has a minimum that occurs at. This minimum value is If , then has a maximum that occurs at. The maximum value is 6. Determine, without graphing, whether the given quadratic function has a max or min value and find it