546 CHAPTER 9 Quadratic Equations, Inequalities, and Functions
Finding the Maximum Height Attained by a ProjectileIf air resistance is neglected, a projectile on Earth shot straight upward with an initial
velocity of 40 m per sec will be at a height sin meters given by
where tis the number of seconds elapsed after projection. After how many seconds
will it reach its maximum height, and what is this maximum height?
For this function, and Use the vertex formula.
Use a calculator.This indicates that the maximum height is attained at 4.1 sec. To find this maximum
height, calculate
Let
Use a calculator.The projectile will attain a maximum height of approximately 81.6 m at 4.1 sec.
NOW TRYOBJECTIVE 5 Graph parabolas with horizontal axes.If xand yare inter-
changed in the equation
the equation becomes
Because of the interchange of the roles of xand y, these parabolas are horizontal
(with horizontal lines as axes).
x= ay^2 +by+ c.
y= ax^2 +bx+ c,
s 1 4.1 2 L81.6
s 1 4.1 2 =-4.9 1 4.1 22 + 401 4.1 2 t=4.1.
s 1 t 2 =-4.9t^2 + 40 t
s 1 4.1 2.
t=
- b
2 a
=
- 40
21 - 4.9 2
L4.1
a=-4.9, b=40, c= 0.
s 1 t 2 =-4.9t^2 + 40 t,
EXAMPLE 7
CAUTION Be careful when interpreting the meanings of the coordinates of
the vertex.The first coordinate, x, gives the value for which the function value, y
or , is a maximum or a minimum. Be sure to read the problem carefully to
determine whether you are asked to find the value of the independent variable, the
function value, or both.
ƒ 1 x 2
Graph of a Horizontal ParabolaThe graph of or is a parabola.
- The vertex of the parabola is.
- The axis is the horizontal line.
- The graph opens to the right if a^70 and to the left if a^6 0.
y=k
1 h, k 2
xay^2 byc xa 1 yk 22 h
NOW TRY
EXERCISE 7
A stomp rocket is launched
from the ground with an
initial velocity of 48 ft per
sec so that its distance in feet
above the ground after
tseconds is
.Find the maximum height at-
tained by the rocket and the
number of seconds it takes to
reach that height.
s 1 t 2 =- 16 t^2 + 48 tNOW TRY ANSWER
- 36 ft; 1.5 sec