Name: Class: Date: Unit 8-9 Review
1. Write y2 – 2x + 10y + 23 = 0 in standard form. Identify the vertex and axis of symmetry,.
2. The height, in feet, of a batted ball can be represented by y = –16x2 + 128x + 2, where x is the time in seconds. What
is the maximum height of the ball?
3. Write the equation in standard form for the circle with center at (–6, 1) and radius 3
4. Sketch the graph of .
5. Write the equation in standard form of the ellipse with foci and .
and if the minor axis has y-intercepts of 6
.
6. For the equation , find the coordinates of the center, foci, and vertices. Then graph the equation.
7. Write the equation for a circle with center (–3, 4) and tangent to y = 5.
8. Write in standard form. Identify the related conic.
9. Write in standard form. Identify the related conic.
10. Graph the hyperbola given by 11. Graph the hyperbola given by 12. Sketch the curve given by the set of parametric equations.
13. Write and in rectangular form. Then graph the equation.
14. Write and in rectangular form. Then graph the equation.
15. Write an equation in slope-intercept form of the line with the given parametric equations.
x = –4t – 9
y = 9t – 7
16. Write y = 2t2 + 2 and x = 7t – 8 in rectangular form.
17. A toy rocket is launched at an initial velocity of 50 ft/s at an angle of 75° with the horizontal. How long will it take for
the rocket to travel 15 feet horizontally?
18. A rock is tossed at an initial velocity of 30 m/s at an angle of 10° with the ground. After 0.5 second, how far has the
rock traveled horizontally and vertically?
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Name: Class: Date: Unit 8-9 Review
19. A golf ball is hit with an initial velocity of 160 ft/s at an angle of 28° with the horizontal. After 1.6 seconds, how far
has the golf ball traveled horizontally and vertically?
20. A discus is thrown from a height of 4 feet with an initial velocity of 65 ft/s at an angle of 44° with the horizontal. How
long will it take for the discus to reach the ground?
21. A projectile is fired from ground level with an initial velocity of 35 m/s at an angle of 35° with the horizontal. How long
will it take for the projectile to reach the ground?
22. Draw a diagram that shows the resolution of the vector described below into its rectangular components. Then find
the magnitudes of the vector's horizontal and vertical components.
23. Find the component form of 24. Find 7r – 4s if r = with initial point B(–3, 2) and terminal point C(–7, 8).
and s = .
25. Let be the vector with initial point J(–15, –10) and terminal point K(–14, –12). Write of the vectors iand j.
as a linear combination
26. Find the component form of the vector v with magnitude 30 and direction angle 240°.
27. Find the direction angle of <–8, 12>.
28. Find the angle θ between u = <6, 3> and v = <2, –6>.
29. Are vectors u = <1, 2> and v = <–6, –5> orthogonal?
30. Draw a diagram of both an ellipse and a hyperbola and label all the important parts. (Look on line for this or in your
textbook)​
31. Practice being able to classify conics. There are multiple questions devoted to this and the questions really should be
easy and quick to accomplish!​
32. Determine the domain of the function 33. Find f(–6) for f(x) = 2x2 + 11x – 5.
34. Find f(m + 2) for f(x) = 2x2 + 7x – 8.
35. Identify the y-intercept and zeros 36. Determine whether the graph of .
has infinite discontinuity, jump discontinuity, point discontinuity,
or is continuous.
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Name: Class: Date: Unit 8-9 Review
37. Determine whether is continuous at 38. Find the average rate of change of f(x) = 39. Find the average rate of change of f(x) = 40. Given f(x) = x2 – 6 and g(x) = .
on [–4, 1]. Round your answer to the nearest hundredth.
on [1, 7]. Round your answer to the nearest hundredth.
, find (g ° f)(–1).
Condense each expression.
41. ln 13 – 7 ln a – 3 ln b + 5 ln c
Solve each equation.
42. log (x – 3) = –2 + log (x + 6)
43. 2.9x = 9.7
44. log 2 (–5x) = log 2 3 + log 2 (x + 2)
45. 46. Analyze f(x) = 3x5. Describe the domain, range, intercepts, end behavior, continuity, and where the function is
increasing or decreasing.
47. Find (x3 – 9x2 – 4x + 36) ÷ (x + 2) by using synthetic division.
.
Answer: _________________________
.
48. Given that one zero is 4, find all zeros of P(x) = x3+ 6x2 – 16x – 96.
.
Answer: ___________________________________
.
49. Locate the asymptotes and graph the rational function 50. Find the domain of and the equations of any vertical or horizontal asymptotes for f(x) = Powered by Cognero
.
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Name: Class: Date: Unit 8-9 Review
Answer Key
1. vertex: (1, –5)
focus: (1.5, –5)
axis of symmetry: y = –5
directrix: x = 0.5
2. 258 feet
3. (x + 6)2 + (y – 1)2 = 45
4. 5. 6. (±
, 0) 7. (x + 3)2 + (y – 4)2 = 1
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Name: Class: Date: Unit 8-9 Review
8. ; 9. ; 10. 11. Powered by Cognero
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Name: Class: Date: Unit 8-9 Review
12. 13. ; 14. ; Powered by Cognero
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Name: Class: Date: Unit 8-9 Review
15. y = x – 16. y = x2 + + 17. 1.2 seconds
18. 14.8 m horizontally and 1.4 m vertically
19. 226.0 feet horizontally and 79.2 feet vertically
20. 2.9 seconds
21. 4.1 seconds
22. 23. <–4, 6>
24. 25. i – 2j
26. <
, >
27. 123.7°
28. 98.1°
29. no
30. 31. 32. 33. f(–6) = 1
34. f(m + 2) = 2m2 + 15m + 14
35. y-intercept: 4.73
no zeros
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Name: Class: Date: Unit 8-9 Review
36. The function has point discontinuity.
37. continuous
38. 0.22
39. 0.13
40. 41. ln 13a –7b –3c5
42. 3.09
43. 2.13
44. –0.75
45. –6
46. D: {x| x }
R: {y| y }
y-intercept: (0, 0)
x-intercept: (0, 0)
symmetric with respect to the origin
odd
continuous
as x , f(x) ; as x , f(x) decreasing: increasing: 47. x2 – 11x + 18 48. The roots of the equation are –4, 4,and –6.
49. horizontal asymptote at Powered by Cognero
vertical asymptotes at Page 8
Name: Class: Date: Unit 8-9 Review
50. D = {x | x ≠ 5, x R}; vertical asymptote: x = 5
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