APPLICATIONS of quadratics (word problems) Flashcards
If f(x)=5x what is f(-3) ?
f(-3)= 5 (-3) = -15
If h(t)= 3x2-8 what is h(2)?
h(2) = 4… 3(2)2-8 = 3(4)-8 = 12-8 = 4
if g(m)= m2-5m what is g(4)
g (4) = -4
42-5(4)=16-20= -4
what are only two things you might be trying to find in projectile problems?
height or time
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)
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)
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)
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..
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).
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)
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)
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).
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.
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)
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
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
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
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
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
Projectile motion: How can you think of h(t)?
the height of the projectile at time t
Projectile motion: How can you think of h(7)?
the height of the projectile at 7 seconds
Projectile motion: How can you think of h(z)?
the height of the projectile at time z
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.
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.
h(t)= -16t2 + 32t +100
what is the initial height? (starting height)
100 ft
h(t)= -16t2 + 32t +100 what is the initial velocity?
32 ft/sec
h(t)= -16t2 + 32t +100 what is the y intercept?
100, It is the initial height
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)
h(t)= -16t2 + 32t +100 what is the “32”
that is the initial velocity, or starting speed (ft/sec)
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,
twice a number
2x
3 less than twice a number
2x-3
the square of a number
x2
twice the square of a number
2x2
5 more than twice the square of a number
2x2+5
6 less than double the square of a number
2x2-6
increased by the number
+x
8 less than triple the square of the sum of a number and 3
3(x+3)2-8
seven less than the square of the sum of a number and 4
(x+4)2-7
the square of the product of number and 8
(8x)2
the sum of the square of a number and 8
x2+8
the sum of twice the square of a number and 13
2x2+13
7 less than a number
x-7
7 more than a number
x+7
What are sides of rectangle when one side is three less than twice the other?
x and 2x-3
what are side of rectangle when one side is 5 less than twice the square of the other?
x and 2x2-5
what are sides of rectangle when one side is four more than the square of the other side?
x and x2+4
what is the perimeter of a rectangle?
distance around.. Add up sides.. l+l+w+w..
Or
P = 2l + 2w
what is the area of a rectangle?
SQUAREA..
Count squares..
Multiply sides..
A= lw
two consectutive integers?
x and x+1
three consecutive even integers?
x, x+2, x+4
three consecutive odd integers?
x, x+2, x+4 (odds are also 2 apart from eachother)
two consecutive even integers?
x, x+2
two consecutive odd integers
x, x+2 (odds are also 2 apart from eachother)
three consecutive integers?
x, x+1, x+2
two consectutive positive integers?
x, x+1 just take the positive answers
three consecutive positive even integers?
x, x+2, x+4 just take the postive answers
three consecutive negative integers?
x, x+1, x+2 just take the negative integers
two consecutive odd positive integers?
x, x+2 just take the positive odds
the product of two consecutive even integers
x ( x+ 2) = x2+2x
the sum of three consecutive odd integers
x + x+2 + x+4
=3x + 6
the product of two consecutive integers
x (x+1)
=x2+x
the sum of two consecutive even integers
x + x + 2
=2x+2
the product of three consecutive even integers
x (x+2)(x+4)
the sum of two consecutive integers
x + x + 1
= 2x + 1
