6.6 Analyzing Graphs of Quadratic Functions

The vertex form of a quadratic function gives us certain information that makes it very easy to graph the function.• Vertex (h, k)• Axis of Symmetry (AOS) x=h• The value of a determines the direction of

opening and the width of the parabola. Multiply a by 1, 3, and 5 to find your slope for more points to graph.

• The parent graph of a parabola is the equation:

• Just like when we examined absolute value functions, the graph of a parabola will translate based on certain values being added, subtracted, or multiplied to our parent graph.

Examples: For each quadratic function, identify the vertex and axis of symmetry. Then, graph the function.

1)

2)

Try these.3) 4)

Examples: Determine whether the following function has a minimum or maximum value. Then state that value.

5) 6)

• When given the vertex of a parabola and point a parabola passes through, we can write the equation for the parabola. The process is similar to writing a linear equation.

• To write the equation for a parabola, substitute the vertex and ordered pair into the vertex form equation, and then solve for a. Then go back to the vertex form equation, and substitute in a, h, and k.

Examples: Write an equation for the parabola with the given vertex that passes through the given point.7) Vertex (-3, 6); passes through (-5, 2)

8) Vertex (2, 0); passes through (1, 4)

Try this.9) Vertex (1, 3); passes through (-2, -15)

Examples: Use transformation rules and the graph to graph the following functions.

10)

11)

12)

Create an equation!

Write an equation for a quadratic in vertex form that meets the following conditions:• has a vertex in the third quadrant• has a maximum value• is wider than the parent graph