Quadratic Test Review Key (1).pdf 5r281b

A lgebra II honors Quadratic Test Review Sheet

3

heading:

r n-calculator Questions Factor the expression completely. If it is not factorable write Prime 1. x 2 - 14.x+ 49

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2.

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3. 4x + 16x + 15

2 x3 - 5 0 x

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Solve the equation by factoring. 4. 6x2 + 18x = 0

5.

2x2 - 5

(iy[k + i ) - O (q x

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x-O

12

x

v ~ Id — O

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o

Y ' V - O

f 5 - O

Y ~ y Solve the equation using the square roots method. (x - 2 ) 2+ 8 = 0

7. 3 ( x - l ) 2 - 2 = 13

3

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I ) 3 --

n ^ j? V ' Iz J J ? ,' x - d - d t J d Solve the equation bv completing the square. 8. x2 - 8 x - 6 = 0 -

Q>

X -

-J5

X'-I +JZ, /]

9. 3x2 - 18x + 3: 3 3 * " - / 0 . pr

+

- - 3 + 3C2J>

3 ^ - 3 ) 0 - 3 I V ' H ~ J~d ^ ~ 10. 1Ox7 - I4x + 4 = 0_ X - %

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> - 3 -

f 11. I

o f

y~ ^

i 2J5;

y - 3 4= > J3-

- 2 x f 2x —6 = 0

X^~ X * 6 j O it J

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Solve the equation using the quadratic formula. 11. 2x2 + 3 x - l - x 2 +5

12. 4x + 2x + 3 = 2x~ - 5 x + 7

3 ><~ 3 -f ~~?y - y -

y3 thx- -

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o = “2 i 9

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Find the discriminant and then describe the nature of the roots. choices are: 2 real roots. 1 real root. 2 imaginary roots 13. 6x2 - 2x + l = 0

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3

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14. 4x2 - 2 0 x + 25 =

b^^C ie

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15. Classify the following numbers. ReaL

-25 *V=4 VI2T

Imaginary

Ratiojjal

Irrational

Integer

Whole

Natural

z

1

2 Vl2

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Solve the quadratic equation using anv method. Each method must be used at least one time. Quadratic Formula. Completing the Square. Factoring, or Square Roots 17. x2 + 3x + 4 = 0

16. 3(x + l)2 - 4 = 20

J o

3

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2 ci

0 ^ 8 h -a jS

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y ~~ ~~ I ~ X I

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v - ~ ( f ^

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18. 6x2 + 1 9 x - 7 = 0

^ 3 i v - ; v ‘ ^ 3 x 0 * ^ ~ ? N) - I

19. 3x + x + 7 = C _ - j ± J o ^ T ? ocr>

F C ttk )f,(n y o ^

^

C

r T

O (&

x

, - / 1 J ^ eJ L* .

/

Fac

(r a c f o / ; / K j 20. x2 + 4 x + 10 = 2 - 5 x J P

f

Q x t d -

o

(3* ^ 9 X

f y f >

21. 4x2 -1 8 x = 0

c?x~O

$

- 9

x

- -

t

1


X ~ O

X ■

3-

C o rr\p [t^ n o 2 f ^

+6 ) > = - 3 . | ^ g , W

Jhe

23. -3 x - 1 2 x - 6 0

?

-3 JZTffc)^F5 -Ko ~ - c J Z

^X-~ Q>~tJIe

X- '(o { iI iJ q,

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o

w

o +

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k + z - n i

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A. (x + 3 ) ( x - 7 ) > 0

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B. 4 x - x 2 > 0 H x - x *Jz-. o kC tf-x}~

3c - "7

* >O 4 =~ J

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V - C/

C. x2 - x - 3 0 < 0 - 3 0

— o

L X -f 6 0 X " -5

- ( d ) *- O ><-6

O

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(/ " 5 / < 0 Simplify the expression. 26. V6 x Vl 2

3

^

3 1 Co ' J a

I &J1*

/


Cs

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25. 3V72

7

27. V -100 ‘v f i-

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y jjtr b r.l c r,9 ') r,3> -c r,o 35. ( 6 - 2 / ) - ( 7 - 5 / ) (j)~ c) l "

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( 37. 4 + 3/) (4 - 3 / )

36. (6 + 0 ( 2 - 4 / )

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3 4 i ' 5 c 4 - 7 c

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38. a. -

34. ( 3 - 5 / ) + ( 1 - 7 / )

3 3 . /9075 9 4 > 8 r,3

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39.

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u-i c 4 + 3/

2-3/ 3-4/

40.

4 - 3 c'

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Graph the following quadratics. Begin by getting the equations in the a]ppropriate form asked and identify the information below. 42. / ( * ) = 4x + 16x + 17 ft

/\

/ „ / L

JL

f M

i W ifl-

- n

t u ) - 1^ !Q> ~ W - V H x ) - / ^J=LL Y Vertex Form:,

Vertex Form:

‘jfC-

vertex:

Vertex:

AofSym:^:^ f

A of Sym: ^

Domain: ( j - CXi f O O ^)

Domain:

Range: C ~ ~ ° 0 , ' 3 ^ 7

Range: L l ," = 0 -1

x-intercept: j )

x-intercept: (f)

y-intercept:

y-intercept: ^ 0 f I

max/min: < r r + K 13 inc

0

< 7 6 < ? f-Y V

dec:

i

V" I j ^ < 3^ ^

- b^y°K )

mai^ram) O n > n inc: C ' d t * 6 )

's

i~^) >

IY *I-

'3 ^

C t > r ) - - ( y - t O ^ - 2^ ) 43. / ( x ) = - x 2 + 2 x + 3

<3,0. 5, V ;

= I

4-h o f suw eki x-cooid-'na-fe. o f f ^ vtfk-x 1y j i he , / ^ k x

l.'dfe

fd )-~ -

3 - I +■ 5 f- 3

' / / / V

V

u e ^ k v ;

N

6 / , S i )

Factored Form: Vertex =0

,< 3 ,0 Axis of Symm:

, ^

in: ( - * 0 , ^ ) Domain -intercept: ^ ^ / inc:

I )

Range:

\

— ( U ^ j

in: P " ) a v

V

dec: T f t

Write the equation o f the quadratic shown. (Don’t forpet stretch or shrink-) S Z < \tX

44

f e r s n '. £ ( x ) - C , f y - h y

i/erh*: (-Q ( (T) $ t * ) - Q C x +\l) s f Q

I 3

p + M , - 3 ^ - i - P

5

H

-

'tc 9 q

f V

3n

r

f - 6

f

44. Write the quadratic equation, in factored form with zeros x = 2 and \x = — .

ik - I

ttx Y - k - d W - D

f(x)-ID

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45. Find the minimum o f / ( x ) = x 2 +8x + 10

i l l o - y 3 f9yl'l(t>

fOO +
All numbers must be integers.

O C C ^ rS ^

- i/<*/ > > r

l/e ' f e * 6

Llf - 6 ^

( he

[ x - m Y - 6

Calculator Questions 46. Graph the following quadratic on your calculator and identify any information below. A graph is provided if you want to draw a sketch o f the graph to help you. / (x) = - 2 x 2 +1 lx - 3 Domain:

^0 , -h

Ma: I a x /M in:

Range: L

1^

(c*, \

G. j~

^ J 3^)

' V ' L < P , ”7 S

*£

Increasing Int:

Decreasing Int : _ Q

Zeros:

47. A ball is thrown upward from the top of a 80 foot cliff with an initial velocity o f 15 feet per second. (This question is continued on the next page) A. Write the equation that models the height o f the ball with respect to t me.

hu y

u s 6 t-e o

B. How long does it take for the ball to reach the ground?

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y -tn k w p k ,

f r

C 'p r/fO Y 'im jfe ^ ^ eccn S i

C. What is the maximum height o f the ball and how long does it take to reach height,? ach this maximum height? fo c g ln lo j ThC P f \a * ( n n < -/n ^ o f b c il\ ,5 a p p r o y lm a ie ('j

.

S n o o d s ,

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A study was done to compare the speed x (in miles per hour) with the mileage y (in miles per gallon) o f an automobile. The results are shown in the table.

Speed x

15

20

25

30

35

40

45

50

5.

60

65

70

75

M ileage^

22.3

25.5

27.5

29.0

28.8

30.0

29.9

30.2

30 .4

28.8

27.4

25.3

23.3

(a)

Find the quadratic model that best fits the data.

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(b)

According to the model, at what speed is the miles per ga Ion is the greatest

(c)

Determine the mileage of a car that is traveling 48 miles per hour.

\ = -'/S

3 nd

yd ' •

J-

-vr v b

3 ° -3 5 j 2 P

According to the model, at what two speeds does the car average 26 miles per gallon?

(d)

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Go /

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0 (3

fa ^

~7

y 3

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-o c

l- O k r ^ e c f

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Be sure to review your word problems. The general types are area/perimeter, right triangles, and “picture frame”.