syscrash2k Posted June 13, 2004 Share Posted June 13, 2004 Hi, I need some help solving this problem: In the Cartesian plane, function g is represented by a parabola.The coordinates of different points of this parabola are given in the table of values below. x | y 1 | 6 3 | 6 5 | 4 7 | 0 Q: What is the y-intercept of function g? The given image is like an upside down version of this one: The image has NO numbers or scale. Thanks in advance. Link to comment Share on other sites More sharing options...
GNRambo Posted June 13, 2004 Share Posted June 13, 2004 so the image is like this one?... Link to comment Share on other sites More sharing options...
syscrash2k Posted June 13, 2004 Author Share Posted June 13, 2004 (edited) so the image is like this one?... Close, except that the given image shows most of the parabola being ABOVE the x axis... I'll see if I can get a better picture. (edit) I've attached a crappy looking mockup. It is very similar to the image that is shown. Edited June 13, 2004 by syscrash2k Link to comment Share on other sites More sharing options...
kioria Posted June 13, 2004 Share Posted June 13, 2004 ** EDIT: LOL, the image you have provided is deceiving. I thought you drew the coordinates given. My mistake. Link to comment Share on other sites More sharing options...
Johnston Posted June 13, 2004 Share Posted June 13, 2004 is da y intercept 5? Link to comment Share on other sites More sharing options...
kioria Posted June 13, 2004 Share Posted June 13, 2004 (edited) -- delete me -- Edited June 13, 2004 by kioria Link to comment Share on other sites More sharing options...
ZTrang Posted June 13, 2004 Share Posted June 13, 2004 Easy enough. (warning: this won't be the "tricky" way to solve the problem, but the most straight-forward way). Simpy use any three points to turn the equation y=ax^2+bx+c into a system of simultaneous equations (by substituting three different values of x and y), and use the three equations to solve for a, b, and c in turn (don't do this yet; keep reading). Once you have the equation, simply plug in x=0 into the equation to find y, which, incidentally, will be c. So, just solve the three simultaneous equations for c, and you will have your y-intercept. Link to comment Share on other sites More sharing options...
Arnaudt Posted June 13, 2004 Share Posted June 13, 2004 Easy ... if it is a parabola then g(x) = ax^2 + bx + c Let's take the first three points you gave (1,6), (3,6) and (5,4) Solving simulatneously the following equations: a+b+c = 6 9a + 3b + c = 6 25a + 5b + c = 4 Gives you that a = -0.25 b = 1 c = 21/4 The y-intercept is therefore the c value (when x = 0) which is 21/4. (To check that this is right, you can take the last known point which is (7,0), and plugging it into y = -0.25x^2 + x + (21/4) gives the right answer, (7,0).) Link to comment Share on other sites More sharing options...
ZTrang Posted June 13, 2004 Share Posted June 13, 2004 Yes, Arnaudt, that is a more thorough explanation of what I suggested, and by using a computer program to check, which gives (0,5.25) for the y-intercept of the polynomial, you have gotten the correct answer to the problem. There might be a trickier answer, but I just like the simple, straightforward method. Link to comment Share on other sites More sharing options...
markwolfe Veteran Posted June 13, 2004 Veteran Share Posted June 13, 2004 (edited) nevermind. Solution given. :p [EDIT: wait. I don't think that soluction is right. The answer for y-intercept shoucl be between 4 and 6, based on the data originally provided] /me goes to work on problem... Edited June 13, 2004 by markjensen Link to comment Share on other sites More sharing options...
syscrash2k Posted June 13, 2004 Author Share Posted June 13, 2004 Sorry guys, but I'm still lost :wacko: Could you please explain step by step? Thanks. Link to comment Share on other sites More sharing options...
tang_tito Posted June 13, 2004 Share Posted June 13, 2004 nevermind.Solution given. :p [EDIT: wait. I don't think that soluction is right. The answer for y-intercept shoucl be between 4 and 6, based on the data originally provided] /me goes to work on problem... 21/4 is 5.25 why is it wrong then? it's between 4 and 6 Link to comment Share on other sites More sharing options...
markwolfe Veteran Posted June 13, 2004 Veteran Share Posted June 13, 2004 21/4 is 5.25why is it wrong then? it's between 4 and 6 (21)/(4)? I thought it said 2 1/4, or 2.25. :pinch: Shouldn't have gone back to edit. :whistle: Link to comment Share on other sites More sharing options...
syscrash2k Posted June 13, 2004 Author Share Posted June 13, 2004 I've solved it a simpler way, with help from a friend :p . We have the line of symmetry (x=2). From x=2, the distance of the given zero is 5 units. We subtract 5 from 2 to get -3, the other zero. Now that we have the two zeros, we can substitute: a(x+3)(x-7)=0 We can choose any point (for example, (3, 6)) a(3+3)(3-7)=0 -24a=6 a=-0.25 y = -0.25(x+3)(x-7) We then substitute 0 into x to find that y = 5.25 Thanks for all the help! Link to comment Share on other sites More sharing options...
ZTrang Posted June 13, 2004 Share Posted June 13, 2004 As I said, there is the straightforward way, and there is the tricky way. The tricky way is often faster to solve, but the straightforward way takes less time, as one can set up the solution more quickly with less thinking. I'm glad you understand the answer, though. Link to comment Share on other sites More sharing options...
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