Lesson 7

Lesson 7 Summary

 

In this lesson you investigated the following questions:

• How can you use a quadratic equation in factored form to solve problems involving the zeros of the corresponding quadratic function or the x-intercepts of the graph of the function?

• How can you find the roots of a quadratic equation by graphing the corresponding quadratic function?

You found that there could be an infinite number of quadratic functions that have the same zeros or x-intercepts. Among those functions, a certain function could be specified by giving the coordinates of a third point on the parabola or by giving the value of a in the function y = a(x − r)(x − s).

 

You also learned that the roots of a quadratic equation are the solutions to the corresponding function equal to zero. The roots have the same values as the x-intercepts of the graph of the corresponding function and the zeros of that function.

 

By changing a function into a corresponding equation with one side equal to zero, you were able to solve for the x-intercepts of the graphs and the zeros of the function. This enabled you to answer questions involving the functions.

 

You learned how to find the x-intercepts of a function using a graphing calculator. You practised using the zero capability of the CALCULATE feature to answer problems involving a variety of situations.

 

In Lesson 8 you will learn a new process for solving quadratic equations to find their roots.