How would I write the equation of a parabola given the following information?
Q. The parabola has roots of 2 and 4 and opens up. It is congruent to y=3x^2. Write the equation of the parabola in y=a(x-p)^2+q form.
Asked by ... - Mon Oct 26 03:25:31 2009 - - 1 Answers - 0 Comments

A. 0 = 3(2 - p)^2 + q 0 = 3(4 - p)^2 + q p = 3, q = -3 Answer: y = 3(x - 3)^2 - 3
Answered by intc_escapee - Mon Oct 26 03:46:44 2009

What is the purpose of a directrix in a parabola?
Q. I know a directrix is a "fixed line equidistant from the parabola" I get that in every reference book and every site I've been to, but I mean... Can't you just draw the parabola without the directrix? What's its use? Why is it there?
Asked by Sammy - Tue Feb 3 06:33:18 2009 - - 2 Answers - 0 Comments

A. A line perpendicular to the axis of symmetry used in the definition of a parabola. A parabola is defined as follows: For a given point, called the focus, and a given line not through the focus, called the directrix, a parabola is the locus of points such that the distance to the focus equals the distance to the directrix.
Answered by jcire17 - Tue Feb 3 06:39:53 2009

How do you determine the formula of a parabola given the vertex?
Q. The problem reads as follows: A parabola opening upward with its vertex at (5,3) and y -intercept equal to 28. Find the formula.
Asked by Enigma - Tue Oct 28 15:47:48 2008 - - 1 Answers - 0 Comments

A. The equation for a parabola opening up or down is: (x - h)^2 = 4a(y - k). The vertex is (h, k). The y-intercept is found by putting x = 0: For your parabola: h = 5, k = 3. The equation is: (x - 5)^2 = 4a(y - 3) Putting x = 0 and y = 28: 25 = 4a * 25 4a = 1 The equation is: (x - 5)^2 = y - 3.
Answered by unknown - Fri Oct 31 11:05:22 2008

How can the motion of a catapult be a parabola?
Q. I need a long explanation, but a simple one. I know gravity cna change the course to shape it like a parabola.
Asked by Jimmy - Mon Apr 23 01:25:46 2007 - - 1 Answers - 0 Comments

A. That's not social science, that's math and basic physics. Social science is the study of people and cultures.
Answered by MagentaStudios.com - Thu Apr 26 10:56:05 2007

What is the difference between a hyperbola and a parabola?
Q. Is the parabola what is created when the conic section is cut directly downwards?
Asked by Chris cc - Wed Nov 22 16:45:20 2006 - - 6 Answers - 0 Comments

A. no thats the hyperbola. a hyperbola has two parts. the parobola is when the conic section is cut parrallel to the conic section so you only ever get one continuous curve. if you cut directly downwards you will get two, unless you go through the intersection when the two parts of the hyperbola then intersect.
Answered by Assaye10 - Wed Nov 22 16:48:51 2006

How to do find an equation for the parabola?
Q. I know that this simple, but I can not get it. I have the vertex of the parabola and I have 2 points on the parabola. So how to I get a formula for the parabola?
Asked by JD - Tue Mar 10 13:16:46 2009 - - 3 Answers - 0 Comments

A. Standard forms for a parabola are: (x-h)^2 = (4c)(y-k) and (y-k)^2 = (4c)(x-h). You can simply put in the coordinates for h and h from your vertex. To get c (the focal length) simply plug one of the two points into the appropriate form from above and solve for c.
Answered by stanschim - Tue Mar 10 13:28:08 2009

How do you solve for the interval notation of a parabola?
Q. I don't get this. We were asked to get the domain and range of a parabola opening upward. How do you get its' interval notation?
Asked by Isawink066 - Mon Aug 24 09:44:35 2009 - - 4 Answers - 0 Comments

A. a vertical parabola (opening upwards or downwards) has a domain of all real numbers, (-infinity, +infinity) if its vertex is V(h,k) and it opens upwards then the vertex is a minimum and the range is [k, +infinity) had it opened downwards the range would have been (-infinity, k] notice you have to use a bracket on k because it includes that value.
Answered by iosephus - Mon Aug 24 09:52:59 2009

By looking at a graph of a parabola. How would one tell what the equation for the line of symmetry is?
Q. Simply put I have a terrible text book that isn't great on showing how. I have a parabola with a line of symmetry x=2. Is that also the equation? If not, How would one develop an equation? Thanks in advance for any assistance.
Asked by Dave C - Sun Jun 15 10:38:12 2008 - - 4 Answers - 0 Comments

A. You look at the graph and determine the equation. X i sonly part of the equation. The axis of symmetry is x= -b/2a. Also, its a vertical line that passes through the changing point. So once you find x, You find coordinates on the graph and then plug them in2 a table of values. Rtom there, you figure out the equation, remember, it'll be a "y= a^2 + b + c" because a parabola means its a quadratic equation! *hope this helps * =]
Answered by blondebabe14 - Sun Jun 15 10:46:09 2008

How do you find an equation of a parabola given 3 points?
Q. I need to know how to figure out an equation for a parabola containing the points (-2,7) (1,2.5) (6,15) i just need ot know how ot do it, i don't need the answer! Just guide lines of how to figure it out! Thanks!
Asked by Jessica B - Tue Oct 7 18:41:46 2008 - - 1 Answers - 0 Comments

A. the equation of the parabola is of the form: y = a x^2 + b x + c where a, b and c are to be determined. you are given that for x= - 2, y=7; for x=1, y=3/2; and for x=6, y=15. Plugging these in the general formula above will give you three linear equations with a, b and c as unknowns. This can be solved by manipulating the linear equations, or by using linear algebra (matrix inversion, etc). good luck.
Answered by Rich J - Tue Oct 7 22:54:45 2008

Finding the equation of a parabola using x intercepts and y intercept?
Q. Ok... So i need a little help with my math homework and need an example done for me please. Anyone who can show the following question with all the steps (and hopefully what you did as well) in fairly easy format best answer chosen. (I'm in grade 10) Find the equation of the parabola: The parabola has x-intercepts of 4 and -2 and a y-intercept of -1 Thanks in advance.
Asked by toxic_pistol - Tue Nov 25 20:22:34 2008 - - 1 Answers - 0 Comments

A. find the equation in x-intercept form: y = a(x-b)(x-c) Where a is some constant, and b and c are the x-intercepts. y = a(x-4)(x-(-2)) = y = a(x-4)(x+2) Now plug in the know y-intercept as a coordinate (0,-1) -1 = a(0-2)(0+2) = a(-2)(2) = -4a a = 1/4 Your final equation: y = 1/4 (x-2)(x+2)
Answered by scikidus - Tue Nov 25 20:27:59 2008

How do you find the focus of a parabola with a parametric equation?
Q. The parabola's parametric equation is as follows: X=2t^2 Y=4t how do you find the focus?
Asked by turtleban - Fri Nov 13 01:06:41 2009 - - 1 Answers - 0 Comments

A. Find X in terms of t and substitute it to t in eq. for Y. Compare to y=4aX
Answered by kanad - Fri Nov 13 01:14:50 2009

How do I perform completing the square on this parabola?
Q. I'm given the equation x^2-2x+8y+9=0 I can do completing the square, but I get something that looks nothing like the standard form of a parabola.
Asked by Ohoneo - Thu Jul 30 22:30:27 2009 - - 1 Answers - 0 Comments

A. (x-1)^2 + 8(y+1) = 0 or 8(y+1) = -(x-1)^2
Answered by kim t - Thu Jul 30 22:35:21 2009

Rotating a parabola 45 degrees to the left?
Q. I am trying to figure out how to rotate a parabola with equation y=x^2+1 45 degrees to the left therefore putting the parabola in the 2nd quadrant. If you have any ideas please let me know thx.
Asked by Nick - Mon May 5 11:59:36 2008 - - 2 Answers - 0 Comments

A. To rotate a graph around the origin by any angle , measured clockwise: Replace x with (x cos - y sin ) Replace y with (x sin + y cos ) In this case, = -45, so we have: x' = (x + y)/ 2 y' = (y - x)/ 2 Substitute into your equation: (y - x)/ 2 = (x + y) /2 + 1 And solve for y if so desired.
Answered by unknown - Mon May 5 12:22:07 2008

Parabola that passes through 3 points and its axis of symmetry is parallel to the x axis?
Q. The parabola passes through points (0,1), (3,2), (1,3) and its axis of symmetry is parallel to the x axis. This is problem 28(h) of chapter 5 of Schaum's Calculus book. The answer is 2(x - (121/40)) = -5(y - (21/10))^2. Please show the procedures necessary to get to this answer, thanks.
Asked by mathviced - Sun Jun 1 14:19:52 2008 - - 1 Answers - 0 Comments

A. Since the axis of symmetry is parallel to the x-axis, the equation for the parabola is of the form x = ay + by + c Put the given three points into this equation to obtain equations for a, b, and c: 0 = a + b + c 3 = 4a + 2b + c 1 = 9a + 3b + c Subtract the second equation from the third, and subtract the second equation from the first, to get two equations for a and b: -2 = 5a + b 3 = 3a + b Subtract to get -5 = 2a -5/2 = a Then b = 3 - 3a = 21/2, c = -(a + b) = -8 x = (-5/2)y + (21/2)y - 8 Now do completing the square to get the form given: x = (-5/2)[y - (21/5)y] - 8 x = (-5/2)[y - (21/5)y + 441/100 - 441/100) - 8 x = (-5/2)(y - (21/10)) + 441/40 - 8 x = (-5/2)(y - (21/10)) + 121/40 x - 121/40 = (-5/2)(y - (21/10)) 2(x - [cont.]
Answered by Ron W - Sun Jun 1 14:50:15 2008

How do you decide how wide the parabola is?
Q. How do you decide how wide the parabola is?
Asked by Pushpendra C - Mon Dec 4 15:06:52 2006 - - 4 Answers - 0 Comments

A. Width of a parabola isn't typically one of the things you look for when finding its properties. The most significant properties of a parabola are: (1) x-intercepts, and (2) vertex For a parabola y = A(x-h)^2 + k, the constant that determines the width (and whether it's facing up or down) is A. For larger values of A, the parabola will be narrow. For small values of A, the parabola will be wide. For negative values of A, the parabola will face downward, and for positive values of A, the parabola will face upward.
Answered by Puggy - Mon Dec 4 15:11:28 2006

How do you go from coordinates from a Parabola to Standard Form?
Q. I have three points on my parabola and I cant figure out how to put them into standard form, my 3 points are (0,0) (35,18) and (24,0).
Asked by orangebanannapeel - Sun Nov 8 14:06:08 2009 - - 1 Answers - 0 Comments

How do you find the equation of a parabola?
Q. The parabola is a parachute. It is 14.2 feet high and 23.4 feet wide. The description says "assume the origin is at the center of the parachute".
Asked by Sou socialista - Sun May 31 14:10:24 2009 - - 2 Answers - 0 Comments

A. Let the x-axis run from -11.7 to 11.7, so the distance is 23.4. (-11.7,0) and (11.7,0) are points in the parabola. The vertex is (0,14.2) The equation of the parabola is (x-h)^2 = a(y-k) , where (h,k) is the vertex. (x-0)^2=a(y-14.2) Since (11.7, 0) lies on the parabola, substitute x=11.7 and y=0 11.7^2 = -14.2 a a= -9.64 x^2=9.64 (y-14.2) x^2+136.888 = -9.64 y y = (-1/9.64) x^2 + 14.2 is the equation of the parabola
Answered by cidyah - Sun May 31 14:34:34 2009

What you can determine about the shape of a parabola from it's equation alone?
Q. What you can determine about the shape of a parabola from it's equation alone?
Asked by Saku - Mon May 12 21:17:35 2008 - - 2 Answers - 0 Comments

A. If the equation has the form y-k = a(x-h) then it is a vertical parabola. If a>0 then the parabola is up-opening. If the equation has the form x-h = a(y-k) then it is a horizontal parabola. If a>0 then the parabola is right-opening.
Answered by unknown - Wed May 14 17:59:11 2008

How to write the vertex form equation of a parabola from three points?
Q. I need help with the process to finding the vertex form equation of this parabola that passes through these three points. Opens up or down, and passes through (3,-7), (6,-37) and (-1,-23)
Asked by tyhigaki - Tue Jun 23 00:45:49 2009 - - 1 Answers - 0 Comments

A. y = ax + bx + c y(3) = a(3) + b(3) + c = -7 y(6) = a(6) + b(6) + c = -37 y(-1) = a(-1) + b(-1) + c = -23 solve linear simultaneous equation above, we get a = -2 b = 8 c = -13 y = -2x + 8x - 13 y' = -4x + 8 vertex point if y' = -4x + 8 = 0 x = 2 y(2) = -5 vertex coordinate is (2,-5)
Answered by Yugiantoro - Tue Jun 23 01:11:23 2009

Why parabola open up or down when a is positive or negative?
Q. In my textbook, I can only find that it stated if the "a" value is positive, the parabola opens up, and when the "a" value is negative, the parabola opens down. I can't find anywhere telling me *why* that is. Can anyone please help?
Asked by Blitzer Warrior - Sat Jun 6 19:17:38 2009 - - 3 Answers - 0 Comments

A. Haha lol i just got taught that a positive a makes a smiley parabola and a negative a makes a frowning parabola. i guess its because with a negative one 4(2^2) will be a negative 4 so it will start lower down.
Answered by unknown - Sat Jun 6 19:26:40 2009