Math 2: Algebra 2, Geometry and Statistics

Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434

Name: Date:

 Chapter  3  Test  Review  –  Answer  Key  

 Practice  Problems  

1. a) The vertex form of the equation of a parabola is 𝑦 = 𝑎(𝑥 − ℎ)! + 𝑘 where (h, k)

are the coordinates of the vertex. b) The standard form of the equation of a parabola is 𝑦 = 𝑎𝑥! + 𝑏𝑥 + 𝑐. To find the

vertex, use !!!!

as the x-value of the vertex. Then plug that value into the original

equation to find the y-value. c) The factored form of the equation of a parabola is 𝑦 = 𝑎(𝑥 − 𝑟)(𝑥 − 𝑠) where r

and s are the roots of the parabola. Average the roots to find the x-value of the vertex. Then plug that value into the original equation to find the y-value.

2. 𝑦 = 7(𝑥 − 3)! − 8

3. 𝑦 = − !!(𝑥 − 4)(𝑥 + 3)

4.

5.

6.  a.  𝑥 = 4,−4   b.  𝑥 = −2   c.  𝑥 = 3,−3, 0   d.  𝑥 = 0,  4,  -­‐4  e.  𝑥 = − !

!, !!   f.  𝑥 = − !

!,− !

!   g.  𝑥 = !"± !"#

!   h.  𝑥 = −5  

i.  no  real  solutions   j.  𝑥 = 1, 6      7.  Quadratic  formula  gives  you  𝑥 = !"± !"

!  or  completing  the  square  gives  you  5± !"

!.  

These  are  equivalent.        

10

–10

–20

–30

–40

–50

–60

–70

–80

–90

–100

–5 5 10

Vertex: A (2, –100)Roots: (0,7) & (0, -3)Y-Intercept: B (0, –84) Mirror Point: C (4, –84)

A

B C

120

100

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60

40

20

–20

–10 –5 5 10

Vertex: A (–3, 121)Line of Symmetry x = -3Roots: (2.5, 0) & (-8.5, 0)Y-Intercept: B (0, 85)Mirror Point: C (–6, 85)

A

BC

E

Math 2: Algebra 2, Geometry and Statistics

Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434

Name: Date:

 

8.  a)  𝑦 = 5 𝑥 + !!

!− !"

!     b)    𝑦 = 3(𝑥 + 3)! − 38  

 9.    

a)  The  highest  the  ball  got  was  !"!!  or  82.8  meters  and  it  reached  that  height  after  !"

!  

or  3.4  seconds.  b)  The  ball  landed  after  !"!! !"

!  or  7.4694  seconds.  

c)  The  25  in  the  equation  means  that  the  initial  height  of  the  ball  was  25  meters  (i.e.  it  was  25  meters  above  the  ground  when  it  was  launched)  d)  

   

80

60

40

20

–20

5 5 10

Math 2: Algebra 2, Geometry and Statistics

Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434

Name: Date:

 Extra  Practice  1.  

 

2.  

 

3.  

 4.  

 

5.  

 e.  No  Real  solutions,  the  discriminant  is  negative.  

 

6.  a  &  b)  Any  equation  with  the  form  𝑦 = 𝑎(𝑥 + 2)(𝑥 − 7)  where  a  is  any  real  number.  c  &  d)  Any  equation  with  the  form  𝑦 = 𝑎 𝑥 − 2 𝑥 + 7  where  a  is  any  real  number.  

7.  Answers  will  vary,  but  must  be  these  equations  multiplied  by  some  real  number.  

 

 

8.  

 

8.  

 8.  

 

8.  

   

8.  

       

Math 2: Algebra 2, Geometry and Statistics

Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434

Name: Date:

 9.  

   

10.  

 

11.  

 

12.  

 

13.  a)  b  =  20  and  c  =  35  (plug  in  values  and  solve  the  system  of  equations)  so  the  equation  is:    ℎ 𝑡 = −5𝑡! + 20𝑡 + 35  b)  The  ball  lands  at  !!! !!

!  seconds  

(remember  that  an  exact  answer  means  DO  NOT  estimate  a  decimal  equivalent)  c)  The  vertex  is  at  (2,  55)  which  means  that  the  ball  reached  its  highest  point  of  55  meters  2  seconds  after  launch.  

14.  a)  After  3  seconds,  the  height  is  67  meters.  b)  The  building  is  100  meters  tall.  c)  The  rocket  will  be  100  meters  at  0  seconds  and  8  seconds.  d)  The  rocket  will  be  160  meters  at  2  seconds  and  6  seconds.  e)  The  rocket  lands  after  10  seconds.  f)  The  vertex  of  the  parabola  is  (4,  180)  so  the  rocket  reaches  its  highest  point  of  180  meters  4  seconds  after  launch