Easy graphing with parabolas seems impossible to defeat

• fotballski
In summary: Again, just draw the graphs on paper and try them out … ._.?5) What is the relation between the graphs and the equations, or how do you find that out?It's kinda like … if you have a graph with a certain equation on it, then the trajectory of a projectile that uses that equation is probably going to be similar to the graph. But again, it's just a hunch!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
fotballski
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 learned 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 business 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

Welcome to PF!

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

Hi Daniel! Welcome to PF!

Yes, so choose easy coefficients (numbers) like 0 1 and 2.
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?

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!

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 = … ? )

too tired … must have cake … :zzz:

I may seem stupid, I'm not, but you see, what I learned last year was that x + x equals 2x and really basic stuff. Can you do an example for me so that I understand?

1. How can I graph parabolas easily?

Graphing parabolas can seem difficult at first, but with some practice and knowledge of the equation, it can become easier. One method is to use the vertex form of the parabola equation, y = a(x-h)^2 + k, where (h,k) is the vertex of the parabola. Another method is to plot a few points and then use symmetry to complete the graph.

2. What if the parabola equation is not in vertex form?

If the parabola equation is not in vertex form, you can use algebraic techniques to rewrite it in that form. This may involve completing the square or factoring out a common factor. Once in vertex form, the vertex and axis of symmetry can be easily identified, making graphing easier.

3. How do I determine the direction of opening for a parabola?

The direction of opening for a parabola is determined by the coefficient of the squared term. If the coefficient is positive, the parabola opens upwards. If the coefficient is negative, the parabola opens downwards. This can also be determined by looking at the sign of the coefficient in front of the x^2 term in the standard form, y = ax^2 + bx + c.

4. Can I graph parabolas on a calculator?

Yes, most graphing calculators have the ability to graph parabolas. You will need to enter the equation in the calculator and make sure the window is set appropriately to see the entire graph. Refer to your calculator's manual for specific instructions on graphing parabolas.

5. What is the importance of graphing parabolas?

Graphing parabolas is an important skill in mathematics and science. It allows us to visually represent and analyze quadratic functions, which have many real-life applications such as in physics, engineering, and economics. Understanding how to graph parabolas also helps with solving quadratic equations and finding important points such as the vertex and intercepts.

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