Chapter 3 Test Review Sheet - Answer Key ·...
Transcript of Chapter 3 Test Review Sheet - Answer Key ·...
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)
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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.
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–100
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Vertex: A (2, –100)Roots: (0,7) & (0, -3)Y-Intercept: B (0, –84) Mirror Point: C (4, –84)
A
B C
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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)
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Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434
Name: Date:
Extra Practice 1.
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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.
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8.
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434
Name: Date:
9.
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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