56.An astronaut on the moon throws a baseball
upward. The altitude (height) hof the ball,
in feet, xseconds after he throws it, is given
by the equation
At what times is the ball 12 ft above the
moon’s surface?
h=-2.7x^2 + 30 x+6.5.
Summary Exercises on Quadratic Equations 573
57.A rule for estimating the number of board feet of lumber that can be cut from a log de-
pends on the diameter of the log. To find the diameter drequired to get 9 board feet of
lumber, we use the equation
Solve this equation for d. Are both answers reasonable?
58.A Babylonian problem asks for the length of the side of a square, where the area of the
square minus the length of a side is 870. Find the length of the side. (Source:Eves,
Howard, An Introduction to the History of Mathematics,Sixth Edition, Saunders College
Publishing.)
Perform the indicated operations. See Sections 5.4, 5.5, and 5.6.
- 7 x 13 - 4 x 2 63. 14 + 3 r 216 - 5 r 2 64. 15 + 2 x 215 - 2 x 2
14 + 6 z 2 + 1 - 9 + 2 z 2 110 - 3 t 2 - 15 - 7 t 2 4 - 16 - 3 k 2
PREVIEW EXERCISES
a
d- 4
4
b
2
=9.
The table summarizes methods for solving a quadratic equation ax^2 +bx+c= 0.
SUMMARY EXERCISESon Quadratic Equations
Method Advantages Disadvantages
- Factoring It is usually the fastest method. Not all equations can be
solved by factoring.
Some factorable polynomials
are difficult to factor.
- Square root It is the simplest method for Few equations are given in
property solving equations of the form this form.
a number.
- Completing It can always be used. (Also, It requires more steps than
the square the procedure is useful in other methods.
other areas of mathematics.)
- Quadratic It can always be used. Sign errors are common
formula because of the
expression.
2 b^2 - 4 ac
1 ax+b 22 =
Solve each quadratic equation by the method of your choice.
- 81 t^2 = 49 5.z^2 - 4 z+ 3 = 0 6.w 2 + 3 w+ 2 = 0
s^2 = 36 x^2 + 3 x=- 1 1 x+ 221 x- 42 = 16
