Lesson 6

1. Lesson 6

1.7. Explore 3

Mathematics 20-2 Modue 3

Module 3: Quadratics

Try This 2

Open “Solving Quadratic Equations: Factoring.” Complete all parts of the lesson. Use the arrows to navigate between screens. Press Enter on your keyboard once you have entered an answer.

How are quadratic functions and quadratic equations related?

Did You Know?

The quadratic function f(x) = ax2 + bx + c can be changed to a quadratic equation by replacing f(x) with 0 to get 0 = ax2 + bx + c.

Since f(x) is another symbol for y, you are replacing y with 0 and finding the x-intercepts. Therefore, 0 = ax2 + bx + c, or ax2 + bx + c = 0, is considered the standard form of a quadratic equation.

You studied quadratic functions in Lessons 1 to 5. You are now starting to work with quadratic equations. As you have seen, solving quadratic equations gives you the roots of the equation. These roots are the x-intercepts or zeros of the related quadratic function.

Self-Check 5

This is a photo of a girl heading a soccer ball.

A header in soccer is not usually aimed at getting the maximum distance. Instead, the ball is being directed to go to a particular place. This allows the player who is heading the ball or the player’s teammate to generate a scoring opportunity.

Suppose the height of a header is given as a function of time, h = −4.9t2 +19.6t, where the time is in seconds and the height is in metres. If the ball is grabbed by the goalkeeper just before entering the net, how long will the ball be in the air?

Assume that the height of the ball when caught is the same as the height when it left the player’s head and that the coordinate axes system has its origin at the player’s head. Solve by factoring.

Answer

Remember that roots refer only to equations—in this case, quadratic equations.

The roots of a quadratic equation have the same value as the x-intercepts of the graph of the corresponding quadratic function.
The roots of the equation have the same value as the zeros of the corresponding quadratic function.

If you haven’t done so already, you may want to add the factoring methods you studied in this lesson to your notes organizer.

If you feel you need a bit more practice, complete Self-Check 6.

Self-Check 6

Complete all or parts of “Check Your Understanding” questions 1 and 2 on page 411 in the textbook. When you finish a question, check your work using the shortened answers given on page 563 of the textbook. If you are still unclear about how to answer some questions, ask your teacher for help.