Page 172

messersmith_power_intermediate_algebra_1e_ch4_7_10

Because this formula represents the distance between two points, we usually use the letter d instead of c. Definition The Distance Formula The distance, d, between two points with coordinates (x1, y1) and (x2, y2) is given by d 2(x2 x1)2 (y2 y1)2. Learn this formula! It is very important. EXAMPLE 4 Find the distance between the points (4, 1) and (2, 5). Solution Begin by labeling the points: (4, 1) x1, y1 x2, y2 , (2, 5) . Substitute the values into the distance formula. d 2(x2 x1)2 ( y2 y1)2 22 (4)2 (5 1)2 Substitute values. 2(2 4)2 (4)2 2(6)2 (4)2 136 16 152 2113 YOU TRY 4 Find the distance between the points (1, 2) and (7, 3). The next method we will learn for solving a quadratic equation is completing the square. We need to review an idea fi rst presented in Section 7.3. A perfect square trinomial is a trinomial whose factored form is the square of a binomial. Some examples of perfect square trinomials are Perfect Square Trinomials Factored Form x2 10x 25 (x 5)2 d2 8d 16 (d 4)2 In the trinomial x2 10x 25, x2 is called the quadratic term, 10x is called the linear term, and 25 is called the constant. 4 Complete the Square for an Expression of the Form x2 bx In a perfect square trinomial where the coeffi cient of the quadratic term is 1, the constant term is related to the coeffi cient of the linear term in the following way: If you fi nd half of the linear coeffi cient and square the result, you will get the constant term. x2 10x 25: The constant, 25, is obtained by 1) fi nding half of the coeffi cient of x; then 2) squaring the result. 1 2 (10) 5 52 25 (the constant) 616 CHAPTER 10 Quadratic Equations and Functions www.mhhe.com/messersmith


messersmith_power_intermediate_algebra_1e_ch4_7_10
To see the actual publication please follow the link above