Graph each function. See Examples 6–8 and the Summary of Graphing Techniques box following Example 9. ƒ(x)=x^2+2

Key Concepts

Quadratic Functions

A quadratic function is a polynomial function of degree two, typically expressed in the form f(x) = ax^2 + bx + c. The graph of a quadratic function is a parabola, which opens upwards if 'a' is positive and downwards if 'a' is negative. Understanding the standard form helps in identifying key features such as the vertex, axis of symmetry, and intercepts.

Graphing Techniques

Graphing techniques involve methods for accurately plotting functions on a coordinate plane. For quadratic functions, techniques include finding the vertex, determining the direction of the parabola, and calculating x- and y-intercepts. These techniques help in sketching the graph and understanding the function's behavior visually.

Vertex and Axis of Symmetry

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction the parabola opens. The axis of symmetry is a vertical line that passes through the vertex, dividing the parabola into two mirror-image halves. Knowing how to find the vertex and axis of symmetry is crucial for accurately graphing quadratic functions.