 # Quadratic Functions Objectives: Graph a Quadratic Function using Transformations Identify the Vertex and Axis of Symmetry of a Quadratic Function Graph.

## Presentation on theme: "Quadratic Functions Objectives: Graph a Quadratic Function using Transformations Identify the Vertex and Axis of Symmetry of a Quadratic Function Graph."— Presentation transcript:

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 and the x-intercepts  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.

Graph each quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, 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, y-intercept, 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