Daughter Needs Help with Homework! Help! --> Quadratic Equations
Jackie Trober
My daughter brought me her Algebra II homework this afternoon - I am
clueless on how to even start helping her. I don't want anybody to
actually do the homework - maybe just explain the basics of quadratic
equations. I will be printing out what you repond with and giving it
to my daughter Jackie (Freshman in High School).
I feel bad I can't help her but she has advanced in math much furhter
then I ever went! I would appreciate any help you can give us!
Thank you in advance!
You can email us at jackie...@katke.com.
Thank you very much!!!
Home work:
15. The third and fourth rockets will both be launched with the given
intital upward velocities in feet per second and are to burst at the
specified altitude in feet.
Third Rocket- Fourth Rocket-
Initial Upward Velocity- 200 200
Bursting Altitude- 450 700
16. a. Write a quadratic equation in standard form to represent the
altitude of the third rocket when it bursts.
b. Write a quadratic equation in standard form to represent the
altitude of the fourth rocket when it bursts.
17. a. Use the quadratic formula to find the fuse time for the third
rocket to the nearest tenth of a second. Explain any unusual results.
b. Use the quadratic formula to find the fuse time for the fourth
rocket to the nearest tenth of a second. Explain any unusual results.
You decide to change the bursting altitude of the fourth rocket so
that the bursting altitude is at least 580 feet.
18. Write a quadratic inequality to indicate that the bursting
altitude must be greater than or equal to 580 feet. Rewrite the
inequality so that one size is 0.
19. Write the related quadratic equation by replacing the inequality
sign with an equal sign. Give the roots of this equation rounded to
the nearest tenth.
Now you must plan the launching and bursting of the next three
fireworks in the show. Their initial upward velocities are given in
the table below.
The Screamer- Mod Quad- Newton's
Glory-
Velocity (feet per second)- 160 200 240
For the safety of the spectators, each rocket must burst at least 350
feet above the ground. At least one rocket should burst at it's
maximum altitude.
22. Give fuse times for the rockets in the table. Show that you have
satisified the safety requirement by finding the bursting altitude of
each rocket. Explain how you found the altitude and times.
23. Let h(t)= -16t^2+ vt where v is positive.
a. Use the discriminant to show that there are always two elapsed
times at which altitude is 0.
b. Use your answer to part a or analysis of quadratic functions to
find the maximum altitude of the rocket.
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William Springer
which I'll reprint here for reference:
Given an equation ax^2 + bx + c = 0,
x = [-b +- sqrt(b^2 - 4ac)]/2a
Obviously the first thing you have to do if your equation is not in the
form above is to rewrite it in that form; you should be famililar with
how to do that by now. If the part under the radical sign is positive,
you have two real solutions; if it is zero, you have one real solution,
and if it is negative you have no real solutions.
> Home work:
>
> 15. The third and fourth rockets will both be launched with the given
> intital upward velocities in feet per second and are to burst at the
> specified altitude in feet.
>
> Third Rocket- Fourth Rocket-
> Initial Upward Velocity- 200 200
> Bursting Altitude- 450 700
>
> 16. a. Write a quadratic equation in standard form to represent the
> altitude of the third rocket when it bursts.
> b. Write a quadratic equation in standard form to represent the
> altitude of the fourth rocket when it bursts.
This doesn't mention where it launches from, so we'll assume that it
launches from the ground. This is a little tricky because it involves
physics, so you need to know the following things:
G = 32 ft/s^2
This says that the force due to gravity is 32 feet per second per
second; acceleration will be -G because gravity is pulling in the
opposite direction of your initial velocity.
x = x_0 + v_0t + 1/2 at^2
This says that position equals initial position plus initial velocity
times time plus 1/2 acceleration times time squared.
Now, if you look at the standard physics equation above, you'll notice
it looks like a quadratic equation, doesn't it? We can replace x_0 with
zero (ground level) and get rid of it, replace x with the bursting
altitude, v_0 with the initial velocity (200 ft/sec) and a with the
acceleration due to gravity (-32 ft/sec^2)
Now, if you want to know how long it will take before the rocket bursts,
simply rewrite in standard form (everything on one side of the equals
sign) and use the quadratic formula to solve for t.
This is pretty advanced work for 9th grade. Good luck!
Chergarj
>clueless on how to even start helping her. I don't want anybody to
>actually do the homework - maybe just explain the basics of quadratic
>equations. I will be printing out what you repond with and giving it
>to my daughter Jackie (Freshman in High School).
>
> third and fourth rockets will both be launched with the given
>intital upward velocities in feet per second and are to burst at the
>specified altitude in feet.
>
> Third Rocket- Fourth Rocket-
>Initial Upward Velocity- 200 200
>Bursting Altitude- 450 700
>
>equation in standard form to represent the
>altitude of the third rocket when it bursts.
General Form would something like s(t)=a*t^2 + b*t + c ;
s(t) is some set of values that depends on t;
s(t) can represent position ( could be vertical position)
t may be used to represent time in seconds.
Standard Form would be someting like s(t)=m(t - h)^2 + k ;
both such Forms represent parabolas. the ^2 notation means "squared", or
exponent of 2.
For your purposes, the basic relationship that applies is :
s(t) = -16*t^2 + v*t + s,
where v is initial velocity, and s is the starting position. Since no
information is implied or given for starting position, s=0, so
your General Form for vertical position is:
s(t) = -16*t^2 + v*t
You could and likely should complete the square for the right hand side to
obtain the standard form. Learning this is one of the fundamental objectives
of intermediate algebra, or Algebra II. In this equation,
-16(t^2 - v*t/(-16)) based on distributive property.
Then, inside the parenthese, ADD (-v/(-16*2))^2, then outside the parenthese,
SUBTRACT (-16)*(-v/(-16*2))^2;
Realize, that you are trying to convert to standard form like to resemble
s(t)==m(t - h)^2 + k so that the (h,k) value can be found, which is the vertex
of a parabola; such parabola is what you can graph, not necessarily the shape
of the path that the rocket takes. The ' k ' value represents the maximum
height, and the ' h ' value is the time required to meet that maximum value.
Realize that reading notation in this format (text on the computer screen) is
more difficult than reading it as you would normally write in on paper.
Tell your daughter to review completing the square from her textbook as she
works on the set of problems.
G C
Ken Starks
<jackie...@katke.com> writes
>Hello!
>
>My daughter brought me her Algebra II homework this afternoon - I am
>clueless on how to even start helping her. I don't want anybody to
>actually do the homework - maybe just explain the basics of quadratic
>equations. I will be printing out what you repond with and giving it
>to my daughter Jackie (Freshman in High School).
>
>I feel bad I can't help her but she has advanced in math much furhter
>then I ever went! I would appreciate any help you can give us!
>Thank you in advance!
These questions are based on such very bad science that the teacher
should be severely taken to task for setting them. We are
supposed to derive quadratic equations from some sort of
free-fall gravity model, which actually does not apply to rockets.
The correct response is: "There is not enough information to solve
the problems".
If you want to toe-the-line and conspire with the teacher, you can
start by creating an equation based on conservation of energy for
a projectile going vertically upwards (no air resistance, no
energy input from engines, no loss of mass from exhaust, no
loss of heat energy, no noise ...) and bursting at the top.
Kinetic energy at ground level = Potential energy at bursting height
Its a quadratic equation, but it has little relation to rocketry.
- -
Ken, __O
-\<,_
(_)/ (_)
Virtuale Saluton.