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Easy graphing with parabolas seems impossible to defeat!

  1. Feb 3, 2009 #1
    I went to a normal and super easy norwegian school. Then, I decided it was too easy, and I went over to the IB system (10th grade)

    Everything is fine beside the math witch is impossible. To make matters worse I have been sick a lot, making followng the current unit impossible. considering the fact that I haven't learnt the basics I don't understand anything of teh assignment I got.

    Can some one help me on the following assignment?
    Se here's the assignment:

    1) Define trajectories of the projectiles. Write 4 different quadratic equations according to following criteria:
    a Must be written in ax ² + bx + c form
    b coefficient of x ² must be negative1
    c 2 of equations must be negative
    d 1 equation are trinomials and not perfect square
    e 1 equation must be binomial difference of perfect square

    2) Verify and make shure that the equations have 2 zeros or more. Explain how you verified it
    3) Draw the graphs represented in the 4 different trajectories. Use the equations for this. The 4 trajectories can be in the same Cartesian plane if clearly laveled and/or color coded. To help you graphingit, here are some hints:
    a A parabola is a symmetrical shape
    b The axis of symmetry goes through the vertex
    c you should use the zeros of the equation and the vertex to help drawing it, plus more points taken logically (5 points in total)
    4) Which of the projectile isit better to use? Why? If needed, create specific contex for the situation.
    5) Analyze the relation between the graphs and the equations. Is there a lien between the shape of the graph and the equations? Could you predict how wide or how high the trajectory would be using only the equations? Make a conjecture about the link between the equations and the trajectories.

    6) using a graphic calculator, verify your hypothesis. Sketch a few parabolas labeled with their equations on a new graph. Analyze your hypothesis using this graph.

    7) Explain how those calculations could be useful in a real life situation. It can be specifically linked to the example given here or for another example where parabolas are used.


    Here is what I don't understand:

    Q for task 1) Can these 4 different quadratic equations be any quadratic equations following the criterias?

    No we come to what I really don't understand. The whole buisness with graphs and zeros and trajectories.

    What is the link beteen an equation like this and a graph??? How do you calculate the graph in the first place (without a calculator)

    2) where are the zeros, how do you get them (?), and how do you verify it?

    3) "Draw the graphs represented in the 4 different trajectories. Use the equations for this."

    How do you calculate and do that with the quadratic equations? what do you need to take care of? Can someone give me an example on how to do it from strt to end, so that I can understand?

    4) How do you find out which projectile is best to use?

    5) What is the relation between the graphs and the equations, or how do you find that out?

    With that information, I think I can figure it out.

    PS! Pleas explane like you would to a five year old. I really have no clue, so using very advanced expressions, signs and language will only confuse me more.

    Regards,

    Daniel
     
  2. jcsd
  3. Feb 3, 2009 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi Daniel! Welcome to PF! :smile:

    Yes, so choose easy coefficients (numbers) like 0 1 and 2. :wink:
    Just draw the graph on paper …

    you know it's a parabola, so you know roughly what it looks like …

    put x = 0,1 2, and so on, calculate what the value is, and plot a curve through those points.

    The zeros are where the graph cuts the x-axis (y = 0) … in other words, they are the values of x for which the quadratic is zero.

    How do you get them? erm … you created the quadratic, so it should be easy! :biggrin:

    Use the quadratic formula, or complete the square , or construct the quadratic by multiplying two easy linear functions (ie (x - a)(x - b), in whcih caese the zeros are at x = … ? :smile:)

    too tired … must have cake … :zzz:
     
  4. Feb 9, 2009 #3
    I may seem stupid, I'm not, but you see, what I learnt last year was that x + x equals 2x and really basic stuff. Can you do an example for me so that I understand?
     
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