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You will explore how to find the solutions to a quadratic function by looking at a graph and finding its roots.

TEKS Standards and Student Expectations

A(7) Quadratic functions and equations. The student applies the mathematical process standards when using graphs of quadratic functions and their related transformations to represent in multiple ways and determine, with and without technology, the solutions to equations. The student is expected to:

A(7)(B) describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions 

Resource Objective(s)

Given a quadratic equation, the student will make connections among the solutions (roots) of the quadratic equation, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the function.

Essential Questions

How can you find the x-intercepts of a quadratic function?

How are the x-intercepts of a quadratic function and the solutions of a quadratic equation related?

How can you find the solution of a quadratic function by looking at the graph?

Vocabulary

 

Quadratic Graphs

Video

Watch the following video that describes key parts of a quadratic graph and the relationships between them. Be sure you have your graphing calculator available. You can use this free online graphing calculator if necessary.

Graphing Quadratic Equations

Graphing Quadratic Equations

Source: 
Graphing Quadratic Equations, MarcWhitaker, YouTube

Reflect

Answer the following questions.  Click on the question to check your answer.

Apply

Matching Activity

If you prefer, click here to download the full-size printable matching activity. Print out the sheet and cut along the dotted lines. Find the roots (solutions) of the quadratic equations by graphing. When you have found the solutions, match each equation to its solution by rearranging and rotating the cards. Click the plus sign on the bottom to check your answer.

Vocabulary Activity

Journal Activity