Parabola Definition and 358 Threads

Homework Statement It seems simple, doesn't it? A bead starts from (0,1/2) and simply slides down the parabola y=(1/2)(x-1)[SUP]2 under gravity. The problem is to get its position rel. to origin in terms of time, ie. r = [x(t),y(t)]. Anyone into this? Homework Equations y' = x-1 = tan...

Homework Statement Identify the x-intercept(s) of the parabola y = (x + 2)2 – 3 Homework Equations The Attempt at a Solution No idea on where to begin and if I would do the same thing with y

Homework Statement Identify the vertex of the parabola y = (x + 2)2 – 3 Homework Equations The Attempt at a Solution I would love to have an attempt but I have gone through my book and notes and I'm still confused on how to do this. If i could see an example even so i can work...

[SIZE="5"][FONT="Arial Black"]SOLVED Homework Statement While going through a question, I came across a function f(x)=5^{x}+5^{-x} I saw its graph through a software. It was a parabola with minimum value 2. Now a question arises in my mind. Every function of the type g(x)=ax^{2}+bx+c...

Here an AP Physics problem that's really bugging me. Homework Statement A particle moves along the parabola with equation y = .5x^2 part a) I believe I did this correct. part b) Suppose that the particle moves with a velocity whose x-component is given by vx = c / (1 + x^2)^.5 Show that...

Can anyone please explain to me what a y vs. t and a v vs. t plot would look like for an object projected vertically upward with an initial velocity of 34.3 m/s? Would the y vs. t plot look like a parabola? Would the v vs. t plot look like a diagonal line starting at 34.3 m/s and ending at...

Can anyone please explain to me what a y vs. t and a v vs. t plot would look like for an object projected vertically upward with an initial velocity of 34.3 m/s? Would the y vs. t plot look like a parabola? Would the v vs. t plot look like a diagonal line starting at 34.3 m/s and ending at...

If you are given (5,0) and (-1,0) as the two x intercepts of a parabola is it possible to find the equation of the parabola? I have tried using the vertex formula for the x co-ordinate which is x = 2 the line of symmetry and plugging in either of these co-ordinates into y = ax^2 + bx + c but...

Homework Statement I am given the parabola y=\frac{x^2}{2} I need to find the equations of the 2 tangents to the parabola that pass through the point A(5,-2) Homework Equations y-y_{1}=m(x-x_{1}) a = \frac{1}{2} therefore: tangents pass through the points...

What equation do you use to find any cordinate on a symetrical parabola? I've been hunting and hunting.. I have the x value. Thanks, Kevin

Homework Statement In a local bar , a customer slides an empty beer mug down the counter for a refill. The bartender is just deciding to go home and rethink his life. He does not see the mug, which slides off the counter and strikes the floor 1.40m from the base of the counter. If the height...

Help me understand the components of a parabola as created by a physical object in normal gravity. The object has some forward velocity, some upward velocity, and at some point some downward velocity. Is this correct? Is it safe to say, therefore, that at some point the parabola's...

Homework Statement The parabola 9x^{2} + 24xy + 16y^{2} + 20x - 15y = 0 has vertex at the origin. Find the coordinates of the points on the parabola that have extreme x-values Homework Equations The Attempt at a Solution To start off, I don't quite understand the question...

Lets consider an ellipse with equation \frac{x^2}{25}+y^2=1 and a parabola with equation y=ax²+bx+c (on the same grid) meet at x = ±4 (y>0). This is in a way that at both points would have identical tangents, of course. In this situation, without making any graphs etc, how can someone...

If you have 3 points of a parabola that are'nt the vertex and the only other information you receive is that the A.O.S is parallel to the y-axis how would you acurately find the equation? Everytime I try, I always end up with odd fractions... the pts are (-3,-4), (-1,-1), (2,3) 2...

Homework Statement Find an equation of the normal line to the parabola y = x^2 - 5x + 4 that is parallel to the line x - 3y = 5. Homework Equations ? All that is relevant is mentioned below AFAIK. The Attempt at a Solution Here is my attempt: http://screencast.com/t/oXxI6JPHv My...

I am trying to determine the tangent of the vertex and the axis of symmetry of a rotated parabola, not knowing the equation of the parabola, and only knowing 3pts the equation has to satisfy. Can anyone help out with this? I have three points, the second is always the vertex, and pt1 and...

This question seems easy enough, but I'm having a hard time getting my mind around it. I want to find the solution to a second order polynomial (parabola) defined by the following criteria... 1) It passes through points a and b 2) At point a the slope of the curve is zero (horizontal) 3)...

Hey guys! I'm new here & browse more thanb I post I have an emergency, and a lot of guys who work in IT are pretty knowledgeable. If you could help me out with my question below I would be so happy! Thanks in advance, Damien. Question: I need the EQUATION of a PARABOLA in the form of y...

Hey, Homework Statement Putnam 1951 A6 Determine the position of a normal chord of a parabola such that it cuts off of the parabola a segment of minimum area. Homework Equations Standard Form of a Parabola {y} = {{{a}{{x}^{2}}} + {{b}{x}} +...

Homework Statement Find an equation for a parabola that passes through the following points. To solve you must use triple elimination, you may check you answer any way you wish Homework Equations The Attempt at a Solution okay so the points given were (1,-2) (-3,10) and (4,31) I...

Hey, Homework Statement How do you derive the equations of the parabola from the general equation of a Conic Section? Homework Equations General Equation of a Conic Section, {{{A}{{x}^{2}}}+{{B}{x}{y}}+{{C}{{y}^{2}}}+{{D}{x}}+{{E}{y}}+{F}} = {0} Where (for a parabola)...

I'm studying up for calculus I this fall, and I found a problem I can't solve. The figure (shown in attachment) shows a circle with radius 1 inscribed in the parabola y=x^2. Find the center of the circle. So far, I have no idea. I could use the derivative to find a tangent line, then set the...

HINT! Parabola An arch is in the shape of a parabola with a vertical axis. The arch is 15 ft high at the center and the 40 ft wide at the base. At which height above the base is the width 20 ft? V(0,15) so my equation becomes: (x-0)^2=-4p(y-15)\rightarrow x^2=-4p(y-15) F(0,15-p) &...

mods please move this topic if this is not in the correct section. thanks. :) the question is: the vertices of the family of parabolas y = x^2 + bx, b is constant, lie on a single parabola. Find equation for that parabola. my teacher require me to provide supporting details & background...

Homework Statement If there is a line from the focus of a parabola such that it makes an angle \theta with the x-axis. It intersects the parabola at a point 'P'. I want to find the focal length of the point P as a function of \theta. The Attempt at a Solution The equation of the parabola is...

Homework Statement A parabolic communications antenna has a focus 6 feet above its vertex. Write an equation for the parabola and find the width of the antenna 9 feet from the vertex. Locate the origin strategically. Homework Equations y= x^2 (parent equation for parabola) The...

Change the equation to standard form. y = x^2 + 8x + 20 I thought this was the standard form for parabolas?? I tried this as the answer but it said it was wrong y = (x+4)^2 +4 Thanks for the help! :-)

Homework Statement Find the point on the parabola y= 4x^2 + 2x - 5 where the tangent line is perpendicular to the line 3x + 2y = 7. Homework Equations The Attempt at a Solution I don't know what to do since I was away the last 3 classes since I was away. Help me please.

Can someone help me with this problem? I already turned it in, knowing it was wrong, and now I want to know how to do it. they gave me three points and no equations and expected me to find the standard form and vertex form of the parabola. i don't remember what the points were, so let's just...

First off this is not a homework or a test problem, I just need some help understanding the problem. "Find the standard form of the equation of the parabola with vertex (2,1) and focus (5,1)." I think you use Y=-1/4x^2 and F(0,p) to find the ax^2 part but I'm confused about how to make...

Homework Statement Let g(x) = x^2 + 12x + 36, a parabola with one zero at x = -6. The parabola moves downward at a rate of 2 units/sec. How fast is the distance between the zeroes changing when they are 10 units apart? Homework Equations g(x) = x^2 + 12x + 36 The Attempt at a Solution...

Hi everyone, I have three points in 3D space, and I would like to find the equation of a parabola that goes between them. My final goal is to sample about 20-25 points that lie on the parabola between these three points (ie, the user of my program will provide 3 points, then I will draw a...

Homework Statement Prove that on the axis of any parabola y^2 = 4ax there is a certain point K which has the property that,if a chord PQ of the parabola be drawn through it ,then \frac{1}{PK^2} + \frac{1}{QK^2} is same for all positions of the chord.Find aslo the coordinates of the point K...

I have a parabola. Now, i need to get the length of aprt of a parabolic segment--that is a quarter of a parabola or 1/10 of a parabola, 3/4 of a parabola or anything How is this possible? Please help

How do you graph the perfect parabola?

Homework Statement How do you figure out the equation of a parabola by only knowing the vertex and ONE of the x intercepts Vertex: (0, -1920) X intercept: (96,0) Help=)

Find all the pairs (x, y)R^2, throught which does not cross any curve : y = - x^2 + (4-2p)x + p^2 . Finding pairs (x,y) are the co-ordinate points . Thanks for help

If given two arbitrary points on a parabola, is there anyway to determine an explicit equation for that parabola. I know there are multiple possible parabolas, but how can I find just one of them?

Find the area of the largest rectangle that can be inscribed in the region bounded by the parabola with equation y= 4 - x^2

I know this is probably really easy, but I can't get the answer. Use the definition of a parabola and the distance formula to find the equation of the parabola with focus (1,2) and directrix x=-1 I know the answer is x=(y-2)^2/4. Can anyone tell me how to get there? Sorry to waste your...

This is my first post here so I hope I put it in the proper place. Here's the basic info on the question. parabolic reflector (like a tv dish) has diameter of 10cm, focus is 2 cm from the vertex. Find the depth. Thanks in advance for an help. I've been stuck on this for a while! Getting...

hi, I have this question which is a challenging problem: in this link you will veiw the graph of the question https://www.physicsforums.com/attachment.php?attachmentid=11650&d=1195680084 the question is to find the center of the circle which it's radius is equal to 1. the parabola...

from a graph of a function ( i obtained the graphg by doing a translation and y-scaling) g(x)= 1/3(x-2)^2 -3 b (x in [2:5]) i can see that g is increasing and so it is a one-one function and an image set is [-3;0]. so therefore the function g has an universe function g^-1 . so i can find...

Homework Statement Can we find the equation to a parabola when two points on it are given,both lying on the same side of the axis of symmetry and also the time of travel between them is given.It is also given that the point travels with uniform velocity along the whole length of the parabola.

Can we find the equation of a parabola when two points on it and the time of travel between the two points are given.It is also given that neither of the two given points is the vertex.

The thing I have noticed is that parabola's angle from the x-axis keeps increasing...meaning the object is decreasing from that direction...if that is the case, then how does it go on in that direction forever even though, its speed going in that direction keeps decreasing? At what rate...

Im In a 1st Year University math class and its been a while since i did this stuff and can't remember if I am doing this question right so any help would be much appreciated. The question is to find all the info from the equation y=2(x-4)^2-3 I used the b+/- b^2 -4ac... equation and ended...

Im In a 1st Year University math class and its been a while since i did this stuff and can't remember if I am doing this question right so any help would be much appreciated. The question is to find all the info from the equation y=2(x-4)^2-3 I used the b+/- b^2 -4ac... equation and ended...