APPLICATIONS of quadratics (word problems) Flashcards Preview

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Flashcards in APPLICATIONS of quadratics (word problems) Deck (66)
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1

If f(x)=5x what is f(-3) ?

f(-3)= 5 (-3) = -15

2

If h(t)= 3x2-8 what is h(2)?

h(2) = 4...      3(2)2-8 = 3(4)-8 = 12-8 = 4

3

if g(m)= m2-5m what is g(4)

g (4) = -4      

42-5(4)=16-20= -4

4

what are only two things you might be trying to find in projectile problems?

height or time

5

If the question asks "when".. What are you given and what are you trying to find?

you must be given a height, and have to find a time.

Plug in the height where h or  h(t) is  and solve for t 

unless finding when at peak.. then just -b/2a

(finding time requires solving quadratic.. Or -b/2a if finding time at peak)

6

If the question asks "what height," what are you given and what are you trying to find?

you are given a time and must find an h.  just plug t in.. (unless asking for peak height, then you have to find -b/2a THEN PLUG THAT NUMBER IN for t)

7

when do you have to solve a quadratic in these problems?

(which is the hard one to find?)

when you are asked "what time?"

finding time is tough because you have to solve a quadratic instead of just plugging in

 (unless asked for time when it reaches peak, then just find -b/2a)

8

Projectile motion: at what time is every projectile at it's maximum height?

at the A.O.S., when t = -b/2a.  That is the time. If they want height, however, then you must plug that into the equation to get height if you want it..

9

Projectile motion: how do you find the maximum height? h(t)= -16t2 + 32t +100

The max is the height (y value) of the vertex. the x value (time) at the vertex is -b/2a. Find it and then plug into function to find h(t).. Which is h(-b/2a).

10

Projectile motion: how would you find height after 3 seconds?

don't do it.. just say how..

h(t)= -16t2 + 32t +100

 plug 3 into function (instead of t), fint h(3)

 

11

Projectile motion: how would you find the time it hits the ground? (don't do it.. just say how)

h(t)= -16t2 + 32t +100

This is when the height is zero because it is on the ground. put 0 where the h(t) is.  and  solve for t.  (you'll have to solve a quadratic)

12

Projectile motion: how do you find at what time it is at its peak? h(t)= -16t2 + 32t +100

The peak is at the vertex, The time is the x value of the vertex (height is y value)   the x values are the TIME. . the time at the peak is always t=-b/2a... that is the time. If you wan't to find the height, however, then you'd have to plug that AOS into the equation to get h (y value).

 

13

Projectile motion: How do you find the time when it is 40 ft high?  (don't do it, just tell how)

h(t)= -16t2 + 32t +100

This is when height = 40, so h(t)=40.  Put 40 where the h(t) is and find the t..  you'll have to solve a quadratic.

14

Projectile motion: How would  you find the time when it is 10 ft high?

h(t)= -16t2 + 32t +100

Finding a time (t) so you want to find when the height is 10, so put 10 where h(t) is... 10 =-16t2 + 32t +100

Solve quadratic for t (start by -10 on each side)

15

Projectile motion: How would you find the height after 10 seconds?

h(t)= -16t2 + 32t +100

plug 10 into function (where the t's are)

h(t)= -16(10)2 + 32(10) +100

16

Projectile motion: What are the only two things you are trying to solve? h(t)= -16t2 + 32t +100

either trying to find height, h(t), or time, t

17

Projectile motion: If you are answering a "when" question, what are you solving for?

time. you want it so you substitute in something for h(t)...you will solve a quadratic

18

Projectile motion: If you are answering a "when" question, what are you given that you can substitute in for?

you are given a height, so you will put that where h(t) is and then solve the quadratic to get the t

19

Projectile motion: If you are answering a "what height" question what are you solving for?

height.. h(t).

You are trying to find a height so you plug in a t

20

Projectile motion: How can you think of h(t)?

the height of the projectile at time t

21

Projectile motion: How can you think of h(7)?

the height of the projectile at 7 seconds

22

Projectile motion: How can you think of h(z)?

the height of the projectile at time z

23

Projectile motion: How can you think of h(0)?

the height of the projectile at time 0, or the STARTING HEIGHT.. The y intercept, the initial height.

24

Projectile motion: If you are answering a "what height" question what information is given and what are you substituting in for?

you are given a time, so you substitute a time in for t and then find the h(t) by just plugging in.

25

h(t)= -16t2 + 32t +100

what is the initial height? (starting height)

100 ft

26

h(t)= -16t2 + 32t +100 what is the initial velocity?

32 ft/sec

27

h(t)= -16t2 + 32t +100 what is the y intercept?

100, It is the initial height

28

h(t)= -16t2 + 32t +100 what is the "-16"

that is the pull of gravity (actually, half of gravity. Gravity pulls at 32ft/sec2 at sea level)

29

h(t)= -16t2 + 32t +100 what is the "32"

that is the initial velocity, or starting speed (ft/sec)

30

h(t)= -16t2 + 32t +100 what is the "100"

that is the initial height, or starting height, height at time=0, or h(0), y intercept,  

31

twice a number

2x

32

3 less than twice a number

2x-3

33

the square of a number

x2

34

twice the square of a number

2x2

35

5 more than twice the square of a number

2x2+5

36

6 less than double the square of a number

2x2-6

37

increased by the number

+x

38

8 less than triple the square of the sum of a number and 3

3(x+3)2-8

39

seven less than the square of the sum of a number and 4

(x+4)2-7

40

the square of the product of number and 8

(8x)2

41

the sum of the square of a number and 8

x2+8

42

the sum of twice the square of a number and 13

2x2+13

43

7 less than a number

x-7

44

7 more than a number

x+7

45

What are sides of rectangle when one side is three less than twice the other?

x and 2x-3

46

what are side of rectangle when one side is 5 less than twice the square of the other?

x and 2x2-5

47

what are sides of rectangle when one side is four more than the square of the other side?

x and x2+4

48

what is the perimeter of a rectangle?

distance around.. Add up sides.. l+l+w+w..

Or

P = 2l + 2w

49

what is the area of a rectangle?

SQUAREA..

Count squares..

Multiply sides..

A= lw

50

two consectutive integers?

x and x+1

51

three consecutive even integers?

x, x+2, x+4

52

three consecutive odd integers?

x, x+2, x+4 (odds are also 2 apart from eachother)

53

two consecutive even integers?

x, x+2

54

two consecutive odd integers

x, x+2 (odds are also 2 apart from eachother)

55

three consecutive integers?

x, x+1, x+2

56

two consectutive positive integers?

x, x+1 just take the positive answers

57

three consecutive positive even integers?

x, x+2, x+4 just take the postive answers

58

three consecutive negative integers?

x, x+1, x+2 just take the negative integers

59

two consecutive odd positive integers?

x, x+2 just take the positive odds

60

the product of two consecutive even integers

x ( x+ 2) = x2+2x

61

the sum of three consecutive odd integers

x + x+2 + x+4 

=3x + 6

62

the product of two consecutive integers

x (x+1)

=x2+x

63

the sum of two consecutive even integers

x + x + 2

=2x+2

64

the product of three consecutive even integers

x (x+2)(x+4)

65

the sum of two consecutive integers

x + x + 1

= 2x + 1

66