Tricky Math Problem.


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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:

parabola.gif

The image has NO numbers or scale.

Thanks in advance.

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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.

post-7-1087142877.gif

Edited by syscrash2k
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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.

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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).)

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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.

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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 by markjensen
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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

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21/4 is 5.25

why 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:

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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!

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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.

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