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Name_
' __
Date _ _ _ _ _ _ Class _ _ _ _ __
,.
Connecting Intercepts and Zeros Practice and Problem Solving: AlB
Solve each equation by writing the related function, creating a table of
values, graphing the related function, and finding its zeroes.
,
9
1. x 2 + 1 = 2x
X'L -
Z K
1-
I
=D
.x ':/
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Solutions: _ _~
X
__-_,-)______
I
0
z.
~
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I
Create a quadratic equation then solve the equation with a related
function. You can use a table, graph, or graphing calculator.
_ /
3, A skydiver jumps out of a plane 5,000 feet above the ground and her
parachute opens 3 ,000 feet above the ground, The function
h(t) = - 16[2 + 5,000, where [represents the time in seconds , gives the
height h,in feet , of the skydiver as she falls When does her parachute
open? Round to the nearest second,
Po...
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i... ,~+ e
12<'~ <,
f;t!he ~
.'
, , "': 4 "
6' t
'l. -f 5 LX"lO ::= 3c:6u
7.. ...-/6l.. L
-C
'Z.­
~ I 2..
~ T I
-L.:fi
-=
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7
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2..
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g c:= Z(-Z)=-1f
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4 . y = -2( x- 3)( x- 1) ~ - 2
y
'-=--
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2
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Write each function in standard form.
X 7..
2 Z
y=( x +1) (x -3) ­
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~~ ) 3, Y = 5( x + 3) (x - 2)
-/0
e,',",-~
t'L
Graph each quadratic function. Then identify the X-intercepts and the
7
axis of symmetry o,!Yacllpara ola. ------. 1, y=(x-1)( x -5J....
0
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)('2..=
5
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leviii Connecting Intercepts and Linear Factors
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t
4 . An astronaut on the moon drops a tool from the door of the landing
ship, The quadratic f!-.Jnction f( x) = _2X2 + 10 models the height of the
tool, in meters , after x seconds , How long does it take the tool to hit the
surface of the moon? Round your answer to the nearest tenth ,
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Name ' --------------------------
Date ____________ Cla ss ____________
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i ii Applying
the Zero Product Property to Soive Equations
l
Practice and Problem Solving: AlB
Find the zeros of each function.
1. f( x) = (x - 3)(x + 5) y:; ')
/
2. f( x ) = x(x - 1)
~::=. -
S
~~C~
3. f(x) = (x + 1 )(x + 1)
= x(x -
~
6. f(x)
3)
y -.:::.
I
4. f(x) = (x - 5)(x + 1) X::=' - \
5. f(x)
';I.~
I
=
-;;: "5
(x - 6)(x + 1) Y ~ 6
c-'" ;>'- - -- )
;J
- - I
I
7
7. f(x) = (x - 11 )(x - 1) 8. f( x) = (x + 13)(x + 5)
;X ::=. ~J '3
I
10 . f( x) = (x - 7)(x + 2) 9. f( x) = (x + 5)(x - 8)
.
~
}?<- - · - 5
;;>
;/ --=
-; - 5 ;;>
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Use the Distributive Property andthe Zero Product Property to,JPtve
L... •
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equations-:--­
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- t H9
11 . f(x)=2x( x -2)+ 14(x-2) ~
~ --"t)C <... -,.L- t-11of-) -=- ~
x - 'z- 7 .
12. f(x)= x(x - 4)-2(x -4) :;:..0
(x- 'f- ) ()i - -z.) -::- 0
0
~-= - 7
13. f(x) = 5x(x - 3) + 25(x - 3) ~c
(><,-'3)Cc,,;>,-+l..<;) =~
x' ~ "3>,
~ ~ )
5' ;.c ==- C+-,
>
,.c ~ L-
14 , f( x) = 3x(x - 7) + 7( x - 7) = G'J (~ - 7){ "'3 )i.. + 7) =: c
><=7 . X-= _ 7/ 3
Solve.
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15. The height of a javelin after it has left the hand of the thrower can be
modeled by the function h = 3(4t - 2)(- t + 4), where h is the height of the t
javelin and t is the time in seconds . How long is the javelin In the air?
3 .S
XCCV~5'
16. The height of a flare fired from the deck of a ship can be modeled by
h = (-4t + 24)(4t + 4) where h is the height of the'flare above water in
feet and t is the time in seconds . Find the number of seconds it takes
the flare to hit the water.
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