first person to answer this correctly get 10 points math problem?

Question

who ever answer this correctly eill get 10 points:
the curve of the graph is a degree 3 polynimial and it goes through the points (5,-1.8) find the polynomial

there is an answer but i forgot how to do it so who ever answer it correctly will get the best answer

Answer 1

I'm sorry, but you haven't supplied enough information. There are an infinite number of 3rd order polynomials that will go through that point.

y = ax^3 + bx² + cx + d

Plug in x = 5, y = -1.8
-1.8 = a(5^3) + b(5²) + c(5) + d
0 = 125a + 25b + 5c + d + 1.8

Basically you have 1 equation and 4 unknowns, so you can set 3 of them to whatever values you like and compute the 4th.

One solution is:
a = 1
b = -4
c = -5
d = -1.8

y = x^3 - 4x² - 5x - 1.8

To confirm, plug in x = 5 and see if you get -1.8:

y = 5^3 - 4(5²) - 5(5) - 1.8
y = 125 - 100 - 25 - 1.8
y = -1.8

Another solution is:
a = 1
b = 1
c = 1
d = -156.8

y = x^3 + x² + x - 156.8

To confirm, plug in x = 5 and see if you get -1.8:

y = 5^3 + 5² + 5 - 156.8
y = 125 + 25 + 5 - 156.8
y = 155 - 156.8
y = -1.8

There you go, I've given you *two* correct answers. You can find the remaining answers on your own. :-)

Answer 2

7/4 + 4/5 x < 49/30 + 7/6 x + 5/6 so multiply throughout by 60 (this gets rid of all those pesky fractions) 105 + 48 x < 98 + 70x + 50 so -43 < 22x so x > -43/22 .

Answer 3

There is no way to solve this. We dont have enough information. I could construct many many polynomials to accomplish this.

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Im glad you are actually willing to reward best answer. I always thought that was the point of the system... but apparently not. Everyone should label their header question like this... it might entice us to answer.

Im just curious what wrong answer will be self-voted best when you fail to select best answer.