Print this chapterPrint this chapter

Lesson 5

1. Lesson 5

1.6. Explore

Mathematics 20-2 M3 Lesson 5

Module 3: Quadratics

 
Explore
 

In question 2.b. of Try This 1, you saw that the values of r and s are equal to the values of the x-intercepts in the factored form of a quadratic function.

 

This shows a graph under the heading y = a(x – r)(x – s) with a > 0. The parabola opens upwards with x-intercepts at r and s and a vertex below the x-axis. This shows a graph under the heading y = – a(x – r)(x – s) with a < 0. The parabola opens downwards with x-intercepts at r and s and a vertex above the x-axis.

 

Recall that quadratic functions can have zero, one, or two x-intercepts. By looking at the factored form of a quadratic function, you can determine the number of x-intercepts.

  • If r and s are different values, there are two x-intercepts.

  • If r and s are equal, there is only one x-intercept and the vertex is on the x-axis.

If there are no x-intercepts, the function cannot be written in factored form.

 

This graphic shows three parabolas. One has two x-intercepts at r and s, which are distinct values. The second has one x-intercept at r, and r and s are equal. The third has no x-intercepts and cannot be written in factored form.

Source: CANAVAN-MCGRATH ET AL. Principles of Mathematics 11, © 2012 Nelson Education Limited. p. 362. Reproduced by permission.

 

zero: a value x in the domain of a function, f, that satisfies the equation f(x) = 0

The x-intercepts correspond to the zeros of the quadratic function. A zero is the value you get for x when you make the function equal to zero.

 

The zeros can be used to determine more information about the function and its graph.

 


textbook

Read “Example 1: Graphing a quadratic function given in standard form” on pages 338 and 339 of the textbook. As you read, consider how the zeros are used to determine the equation of the axis of symmetry and the vertex of the parabola.

Self-Check 1
  1. Complete “Check Your Understanding” question 1 on page 346 of your textbook. Answer

  2. Complete “Check Your Understanding” question 2 on page 346 of your textbook. Answer

  3. Complete “Practising” question 4 on page 346 of your textbook. Answer

  4. Complete “Practising” question 7 on page 347 of your textbook. Answer