Lesson 11: 9-1 Graphing Quadratic Functions

-What two characteristics of parabola are found by using the expression b/2a?
-Will the domain of every quadratic function be all real numbers?
-Will a parabola that opens up have a maximum?

Quadratic function
Standard form
Parabola
Axis of symmetry
Vertex
Minimum
Maximum

F.IF.4 For a fucntion that models a relationship between two quanities, interpret key features of graphs and tables in terms of quantities, and sketch graphs showing key features given verbal descriptionof the relationship.

SAT questions related to solving quadratrics: 2-3-13,3-3-14,1-3-16,5-3-3,8-3-16,1-4-25; analyzing graphs: 3-4-12,8-3-11,8-4-19,6-3-11

The maximum or minimum point of a parabola is called the vertex. When a quadratic function is written in standard form y=ax^2 +bx +c, and a is positive, the parabola opens upward, and the vertex is minimum. When a is negative, the parabola opens downward, and the vertex is maximum.

The Innovention Foundation in Epcot's Futureworld in Orlando, Florida, is an elaborate display of water, light, and music. The sprayers shoot water in shapes that can be modeled by quadratic equations. You can use graphs of these equations to show the path of the water.

-Minimum/Maximum - Don't forget to find both coordinates of the vertex (x,y). The minimum or maximum value is the y-coordinate.
-Preventing errors - Tell students that their sketches of parabolas do not have to be perfect. However, students should not "connect the dots" with straight lines. The important thing is for the curve to pass through the graphed order pairs.

If studnets need visual to understand the concept of vertex and the axis of symmetry, then ask students to make a table of values and graph a quadratic equation on a grid papaer. Have students hold their papaers up to the light and fold their parabola in half so that the two sides match exactly. Have students use the crease on their unfolded paaper to locate the vertes, axis of symmetry, and minimum/maximum value.

Define the vocabulary words in the lesson and provide examples and explanations. Say the terms out loud and have students repeat the words. Then have students write the words in their notes.

Allow students to use search engine to find images for each vocabulary term. Have pairs of students choose a representative image for each term to share with the class. Ask them why their image represents the term.

Practice: Exercises 1 - 21

Exercises 68-74

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