Beginning Algebra, 11th Edition

69. 70.

71. 72.

Brain Busters Solve each equation, and check your solutions.

Galileo’s formula describing the motion of freely falling
objects is

.

The distance d in feet an object falls depends on the time t
elapsed, in seconds. (This is an example of an important
mathematical concept, thefunction.)

79. (a)Use Galileo’s formula and complete the following
    table. (Hint:Substitute each given value into the
    formula and solve for the unknown value.)

d= 16 t^2

6 x^212 x+ 32 = 412 x+ 32 + 5 x 12 x+ 32

6 p^21 p+ 12 = 41 p+ 12 - 5 p 1 p+ 12

1 x+ 322 - 12 x- 122 = 0 14 y- 323 - 914 y- 32 = 0

12 x 22 = 12 x+ 422 - 1 x+ 522 5 - 1 x- 122 = 1 x- 222

x^2 + 1 x+ 122 = 1 x+ 222 1 x- 722 +x^2 = 1 x+ 122

3 x 1 x+ 12 = 12 x+ 321 x+ 12 2 x 1 x+ 32 = 13 x+ 121 x+ 32

SECTION 6.5 Solving Quadratic Equations by Factoring 399

t in seconds 0123

d in feet 0 16 256 576

(b)When ,. Explain this in the context of the problem.

80.When you substituted 256 for dand solved the formula for tin Exercise 79,you should
have found two solutions: 4 and - 4. Why doesn’t - 4 make sense as an answer?

t= 0 d= 0

EXERCISES 81– 82

In Section 3.2,we showed how an equation in one variable can be solved with a

graphing calculator by getting 0 on one side and then replacing 0 with y to get a

corresponding equation in two variables. The x-values of the x-intercepts of the graph

of the two-variable equation then give the solutions of the original equation.

Use the calculator screens to determine the solution set of each quadratic equation.

Verify your answers by substitution.

81.

82. 2 x^2 - 7.2x+6.3= 0

x^2 +0.4x-0.05= 0

TECHNOLOGY INSIGHTS