Download x2-3x-18:ox * 3:0 or x - 6:0 Zero Product PtoPefi x:-3 x

Solve a Quadratic lnequality Algebraically
.
Solve x2 - 3x 318 algebraically.
Solving Quadratic
lnequalities
Algebraically The
solution set of a
quadratic inequality
Step
I
Solve the related quadratic equation x2
x2-3x:1.8
is
x
test points satisfy
the inequality.
Step
2
* 3:0
x:-3
:
\8'
Subtract 18 lrom each side.
(r+3Xx-6) =0
It is the empty set
when none of the
3x
Related quadratic equation
x2-3x-18:o
all real numbers when
all three test points
satisfy the inequality.
-
Factor.
or x - 6:0
x:6
Zero Product PtoPefi
Solveeachequation,
Plot -3 and 6 on a number line. Use dots since these values are solutions of the
original inequality. Notice that the number line is divided into tfuee intervals.
-3 <x<6
-6-5-4-3-2-1 0 1 2 3 4 5 6 7 I I
Step
f
Test a value from each interval to see
if it satisfies the original inequality.
x<-3
Test r : -5.
*-zx<L8
-3 <x36
Test r = 0.
x2-3x<18
(_5)2_3(_5)e18
lsyz-3(0)&18
0<18
40 $1.8
The solution set is
x>6
r : 8.
x2-gx<1.8
Test
(8)2-3(8)218
40*78
{r | -3 < x < 5}. This is shown on the number line below
ttt
-6-5-4-3-2-1 0 1 2 3 4 5 6 7 B 9
uidedi:Practice
Solve each inequality algebraically.
A.
Example I
P.rt2
Examples
z
and
t
PP. rtt-rl4
x2+5x<-6
e.
*+
11r+30>0
p eersonal
Tutor gleltge.oom
Graph each inequality.
l. y<x2-8x+2
2.
y>x2+6x-2
5.
y>-x2+4x+1.
Solve each inequality by graphing.
4.0<x2-5x+4
6. -2x2 - 2x + 12> 0
8. SOCCER A midfielder
8r+15<0
7.0>2x2-4x+1
5. x2+
kicks a ball toward the goal during a match. The height of the ball
in feet above the ground h(t) at tirne I can be represented by h(t) : -0.1.t2 + 2.4t + 7.5.
If the height of the goal is 8 feet, at what time during the kick will the ball be able to
Example 4
p.514
enter the goal?
Example 5
Solve each inequality algebraically.
p.515
g. x2+6x-16<0
*
-r'
-t
12x
>
28
to.
12. x2 x2
1.4x>
-49
4x <2L
Lesson 5-8 Quadratic
lnequalities 315