worksheet 2.3-2.8 math 103ml fall 2016 name · worksheet 2.3-2.8 math 103ml fall 2016 name_____...

WORKSHEET 2.3-2.8Math 103MLFALL 2016

Name___________________________________

PREP HOMEWORK.

1) See Piazza for video link.

What is a quadratic function? Write in standard notation with a, b, and c as the coefficients.

2) What is the quadratic formula?

3) What is the discriminant of quadratic function f(x) = ax2+bx+c?

4) Characterize the types of zeros that a quadratic function have depending on its discriminant.

Discriminant > 0

Discriminant = 0

Discriminant < 0

5) How does one find the point(s) intersection of the graphs of f(x) and g(x) algebraically?

6) Write both the standard form and the vertex form of quadratic function.

How do you find the vertex of a quadratic function if the standard form is known?

When does the graph of a quadratic function opens up? Opens down?

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7) What is the maximum value or the minimum value of the quadratic function?

How do you find the maximum value or the minimum value of a quadratic function?

8) How do you solve a quadratic inequality?

9) When does a quadratic function have complex zeros?

What kind of complex numbers can be the zeros of a quadratic function?

10) Summarize the steps you're taking when solving an absolute value inequality.

2

Solve f(x) = g(x). Find the points of intersection of the graphs of the two functions.11) f(x) = 5x + 6

g(x) = x211)

12) f(x) = 4x + 5g(x) = x2

12)

13) f(x) = x2 - 12x + 27g(x) = 2x2 - 12x + 18

13)

14) f(x) = x2 - 13x + 36g(x) = 2x2 - 16x + 32

14)

15) f(x) = x2 + 9x + 19g(x) = 19

15)

Find the real zeros, if any, of each quadratic function using the quadratic formula. List the x-intercepts, if any, of thegraph of the function.

16) H(x) = 3x2 - 20x - 7 16)

17) H(x) = 5x2 - 29x - 6 17)

18) h(x) = x2 - 6x + 34 18)

Find the zeros of the quadratic function using the Square Root Method. List the x-intercepts of the graph of thefunction.

19) F(x) = x2 - 10 19)

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20) g(x) = (x - 4)2 - 16 20)

21) G(x) = (2x - 5)2 - 121 21)

Use factoring to find the zeros of the quadratic function. List the x-intercepts of the graph of the function.22) f(x) = x2 + 5x - 84 22)

23) F(x) = x2 - x - 72 23)

24) g(x) = 64x2 - 1 24)

Solve the problem.25) The length of a vegetable garden is 10 feet longer than its width. If the area of the garden

is 75 square feet, find its dimensions.25)

26) A ball is thrown vertically upward from the top of a building 112 feet tall with an initialvelocity of 96 feet per second. The distance s (in feet) of the ball from the ground after tseconds is s = 112 + 96t - 16 t2. After how many seconds does the ball strike the ground?

26)

27) As part of a physics experiment, Ming drops a baseball from the top of a 310-footbuilding. To the nearest tenth of a second, for how many seconds will the baseball fall?(Hint: Use the formula h = 16 t2, which gives the distance h, in feet, that a free -fallingobject travels in t seconds.)

27)

4

Determine the quadratic function whose graph is given.28)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

Vertex: (1, 4)y-intercept: (0, 3)

28)

29)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

Vertex: (1, 4)y-intercept: (0, 3)

29)

30)

x

y

(-2, -1)

(0, 3)

x

y

(-2, -1)

(0, 3)

30)

5

31)

x

y

(2, -2)

(0, 2)

x

y

(2, -2)

(0, 2)

31)

Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value andthen find that value. Explain your reasoning.

32) f(x) = 3x2 + 2x - 7 32)

33) f(x) = 3x2 + 2x - 6 33)

34) f(x) = -5x2 - 10x 34)

Solve the problem.35) You have 168 feet of fencing to enclose a rectangular region. Find the dimensions of the

rectangle that maximize the enclosed area.35)

36) A developer wants to enclose a rectangular grassy lot that borders a city street forparking. If the developer has 356 feet of fencing and does not fence the side along thestreet, what is the largest area that can be enclosed?

36)

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37) A projectile is fired from a cliff 400 feet above the water at an inclination of 45 ° to thehorizontal, with a muzzle velocity of 240 feet per second. The height h of the projectile

above the water is given by h(x) = -32x2

(240)2 + x + 400, where x is the horizontal distance of

the projectile from the base of the cliff. Find the maximum height of the projectile.

37)

Graph the function using its vertex, axis of symmetry, and intercepts.38) f(x) = x2 + 12x + 36

x-10 -5 5 10

y40

20

-20

-40

x-10 -5 5 10

y40

20

-20

-40

38)

Vertex = Axis of symmetry =

x-intercepts = y-intercept

39) f(x) = -x2 - 4x + 5

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

39)



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40) f(x) = 2x2 + 8x + 13

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

40)



41) f(x) = 3x2 + 12x + 15

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

41)



Find the vertex and axis of symmetry of the graph of the function.42) f(x) = -4x2 + 16x 42)

43) f(x) = -x2 + 2x - 7 43)

44) f(x) = -2x2 + 4x + 3 44)

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Solve the inequality.45) x2 - 4x - 12 ≤ 0 45)

46) x2 + 3x - 10 > 0 46)

47) x2 - 8x ≥ 0 47)

Solve the problem.48) If h(x) = x2 - 9x + 20 , solve h(x) > 0. 48)

49) The revenue achieved by selling x graphing calculators is figured to bex(31 - 0.2x) dollars. The cost of each calculator is $15. How many graphing calculatorsmust be sold to make a profit (revenue - cost) of at least $275.00 ?

49)

50) A coin is tossed upward from a balcony 320 ft high with an initial velocity of 32 ft/sec.During what interval of time will the coin be at a height of at least 80 ft? (h = -16t2 + vot +ho.)

50)

Find the complex zeros of the quadratic function.51) f(x) = x2 - 25 51)

52) h(x) = x2 + 6x + 45 52)

53) h(x) = x2 + 10x + 34 53)

54) g(x) = 2x2 - x + 5 54)

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Solve the equation. Graph the solution set.55) ∣x∣ = -0.5 55)

56) ∣x∣ = 0.22 56)

57) ∣b + 8∣ - 5 = 3 57)

Solve. Note: the answer key is incorrect. LOL.58) If f(x) = (solid line) and g(x) =(dashed line),

find when f(x) = g(x) and

when f(x) <g(x). Note: the answer key is incorrect.

x-10 -5 5 1 0

y

1 0

5

-5

-10

x-10 -5 5 1 0

y

1 0

5

-5

-10

58)

59) If f(x) = (solid line) and g(x) =(dashed line),



x-10 -5 5 1 0

y

1 0

5

-5

-10

x-10 -5 5 1 0

y

1 0

5

-5

-10

59)

10

60) If f(x) = -∣x∣ (solid line)and g(x) = 3 (dashed line),



x-15 -10 -5 5 10 15

y

10

5

-5

-10

x-15 -10 -5 5 10 15

y

10

5

-5

-10

60)

61) If f(x) = -∣x∣ (solid line)and g(x) = 5 (dashed line),



x-10 -5 5 1 0

y

1 0

5

-5

-10

x-10 -5 5 1 0

y

1 0

5

-5

-10

61)

11

62) If f(x) = x2 (solid line)and g(x) = 5 (dashed line), find when f(x) = g(x) and when

f(x) <g(x). Note: the answer key is incorrect.

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

62)

63) If f(x) = x2 (solid line)and g(x) = 6-x2 (dashed line), find when f(x) = g(x) and


x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

63)

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64) So you want to compete with Leonard's Bakery and got yourself a truck and an ancientmalasada recipe from your tutu. You're ready to start your malasada food truck, andyou're going to call it Donatello's Bakery.

You want to find the price and the number of malasadas you need to sell to maximizethe profit. After a few trials changing the price and the number sold, your revenuelooks like this.

Trial# Number Sold Revenue1 120 2252 200 3453 250 3754 300 4375 420 4806 480 4827 500 4768 550 4409 650 374

a. What is a good function to approximate the revenue as a function of the number ofmalasada sold. (Hint: desmos, curve of best fit. Also hint: the revenue for selling 0malasada should be 0, so the function modeling this should pass the origin.)

b. Call your revenue function in part a R(q), where q is the quantity of malasadas sold.Now, revenue is the price you sell each malasada times the number sold. So, R(q) isreally a product of the price function p, the price when q malasadas are sold times thenumber sold q, R(q) = q ∙ p. The price function p is a linear function of q, so call it p(q).

You don't know the price function p(q) but you can figure out p(q) from your functionR(q) in part a by factoring out q. What is your price function p(q)?d. The cost to make each malasada is 25 cents, and the total cost to run the truck is $50and to pay Roman to work for you for the day is $100.

What is the cost function C(q) as a function of the number of malasadas sold q?

e. What is the profit function P(q)? Remember profit is Revenue-Cost.

f. What is the number of malasada you should sell per day to maximize the profit?

And what should the price per malasada be?

64)

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Answer KeyTestname: HW-2328-FALL16

1)Objective:

2)Objective:

3)Objective:

4)Objective:

5)Objective:

6)Objective:

7)Objective:

8)Objective:

9)Objective:

10)Objective:

11) x = -1, x = 6Objective: (2.3) Find the Point of Intersection of Two Functions


13) x = 3, x = -3Objective: (2.3) Find the Point of Intersection of Two Functions

14) x = 4, x = -1Objective: (2.3) Find the Point of Intersection of Two Functions


16) x = - 13, x = 7

Objective: (2.3) Find the Zeros of a Quadratic Function Using the Quadratic Formula

17) x = - 15, x = 6

Objective: (2.3) Find the Zeros of a Quadratic Function Using the Quadratic Formula18) No real zeros or x-intercepts

Objective: (2.3) Find the Zeros of a Quadratic Function Using the Quadratic Formula

19) x = 10, x = - 10Objective: (2.3) Find the Zeros of a Quadratic Function Using the Square Root Method

20) x = 0, x = 8Objective: (2.3) Find the Zeros of a Quadratic Function Using the Square Root Method

21) x = -3, x = 8Objective: (2.3) Find the Zeros of a Quadratic Function Using the Square Root Method

22) x = -12, x = 7Objective: (2.3) Find the Zeros of a Quadratic Function by Factoring

23) x = -8, x = 9Objective: (2.3) Find the Zeros of a Quadratic Function by Factoring

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24) x = 18, x = - 1

8Objective: (2.3) Find the Zeros of a Quadratic Function by Factoring

25) 5 ft by 15 ftObjective: (2.3) Solve Equations That Are Quadratic in Form

26) 7 secObjective: (2.3) Solve Equations That Are Quadratic in Form

27) 4.4 secObjective: (2.3) Solve Equations That Are Quadratic in Form

28) f(x) = -x2 + 2x + 3Objective: (2.4) Find a Quadratic Function Given Its Vertex and One Other Point

29) f(x) = -x2 + 2x + 3Objective: (2.4) Find a Quadratic Function Given Its Vertex and One Other Point

30) f(x) = x2 + 4x + 3Objective: (2.4) Find a Quadratic Function Given Its Vertex and One Other Point

31) f(x) = x2 - 4x + 2Objective: (2.4) Find a Quadratic Function Given Its Vertex and One Other Point

32) minimum; - 223

Objective: (2.4) Find the Maximum or Minimum Value of a Quadratic Function

33) minimum; - 193

Objective: (2.4) Find the Maximum or Minimum Value of a Quadratic Function34) maximum; 5

Objective: (2.4) Find the Maximum or Minimum Value of a Quadratic Function35) 42 ft by 42 ft

Objective: (2.4) Find the Maximum or Minimum Value of a Quadratic Function

36) 15,842 ft2Objective: (2.4) Find the Maximum or Minimum Value of a Quadratic Function

37) 850 ftObjective: (2.4) Find the Maximum or Minimum Value of a Quadratic Function

38) vertex (-6, 0)intercepts (0, 36), (-6, 0)

x-10 -5 5 10

y40

20

-20

-40

x-10 -5 5 10

y40

20

-20

-40

Objective: (2.4) Graph a Quadratic Function Using Its Vertex, Axis, and Intercepts

15


39) vertex (-2, 9)intercepts (1, 0), (- 5, 0), (0, 5)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

Objective: (2.4) Graph a Quadratic Function Using Its Vertex, Axis, and Intercepts40) vertex (-2, 5)

intercept (0, 13)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

Objective: (2.4) Graph a Quadratic Function Using Its Vertex, Axis, and Intercepts41) vertex (-2, 3)

intercept (0, 15)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

Objective: (2.4) Graph a Quadratic Function Using Its Vertex, Axis, and Intercepts42) (2, 16); x = 2

Objective: (2.4) Identify the Vertex and Axis of Symmetry of a Quadratic Function43) (1, -6) ; x = 1

Objective: (2.4) Identify the Vertex and Axis of Symmetry of a Quadratic Function

16


44) (1, 5) ; x = 1Objective: (2.4) Identify the Vertex and Axis of Symmetry of a Quadratic Function

45) [-2, 6]Objective: (2.5) Solve Inequalities Involving a Quadratic Function

46) (-∞, -5) or (2, ∞)Objective: (2.5) Solve Inequalities Involving a Quadratic Function

47) (-∞, 0] or [8 , ∞)Objective: (2.5) Solve Inequalities Involving a Quadratic Function

48) (-∞, 4) or (5 , ∞)Objective: (2.5) Solve Inequalities Involving a Quadratic Function

49) {x∣25 < x < 55}Objective: (2.5) Solve Inequalities Involving a Quadratic Function

50) 0 ≤ t ≤ 5Objective: (2.5) Solve Inequalities Involving a Quadratic Function

51) x = 5, x = -5Objective: (2.7) Find the Complex Zeros of a Quadratic Function

52) x = -3 + 6i, x = -3 - 6iObjective: (2.7) Find the Complex Zeros of a Quadratic Function

53) x = -5 + 3i, x = -5 - 3iObjective: (2.7) Find the Complex Zeros of a Quadratic Function

54) x = 14

± 394

i

Objective: (2.7) Find the Complex Zeros of a Quadratic Function55) ∅

Objective: (2.8) Solve Absolute Value Equations56) -0.22, 0.22

Objective: (2.8) Solve Absolute Value Equations57) {-16, 0}

Objective: (2.8) Solve Absolute Value Equations58) f(x) = g(x) when x = 2 and x = -2

f(x) > g(x) when x < -2 or x > 2Objective: (2.8) Solve Absolute Value Inequalities

59) f(x) = g(x) when x = 4 and x = -4f(x) > g(x) when x < -4 or x > 4Objective: (2.8) Solve Absolute Value Inequalities





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worksheet 2.3-2.8 math 103ml fall 2016 name · worksheet 2.3-2.8 math 103ml fall 2016 name_____...

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