APPLICATIONS of quadratics (word problems) Flashcards

1
Q

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

A

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

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2
Q

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

A

h(2) = 4… 3(2)2-8 = 3(4)-8 = 12-8 = 4

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3
Q

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

A

g (4) = -4

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

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4
Q

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

A

height or time

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5
Q

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

A

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)

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6
Q

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

A

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)

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7
Q

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

(which is the hard one to find?)

A

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)

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8
Q

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

A

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..

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9
Q

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

A

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).

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10
Q

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

don’t do it.. just say how..

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

A

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

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11
Q

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

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

A

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)

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12
Q

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

A

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).

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13
Q

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

A

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.

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14
Q

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

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

A

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)

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15
Q

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

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

A

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

h(t)= -16(10)2 + 32(10) +100

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16
Q

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

A

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

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17
Q

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

A

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

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18
Q

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

A

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

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19
Q

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

A

height.. h(t).

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

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20
Q

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

A

the height of the projectile at time t

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21
Q

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

A

the height of the projectile at 7 seconds

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22
Q

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

A

the height of the projectile at time z

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23
Q

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

A

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

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24
Q

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

A

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

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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