Question

Find the real numbers a b c such that the graph of the function y=ax^2+bx+c contains the points (-2,-4),(1,-1),(3,-19)

Answer 1

there are a few methods which could work ... which ones are you learning?

Answer 2

Not sure

Answer 3

itd be useful if you had some knowledge of the material to work off of ...

Answer 4

a=34/9 b=31/9 c=-74/9

Answer 5

thats what i calculated may be wrong tho but do u know how to solve it to start with?

Answer 6

you will replace the values, get 3 equations then equate one of them like c=..... then get the other 2 equations then use elimination or so

Answer 7

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Answer 8

and thats not what i get as solutions :)

Answer 9

I know I have to put them in equations just don't know where to start

Answer 10

i tend to start with a setup that will use all the points, but zero out things that im not interested in:

(-2,-4) (1,-1) (3,-19)

when x = the given values, i want certain parts to be zero

y = c1 (x-1)(x-3) + c2 (x+2)(x-3) + c3 (x+2)(x-1)

each x value will zero out one of the constants allowing us to determine the remaining constant

but this is time consuming

Answer 11

for (-2,-4)

-4 = c1 (-2-1)(-2-3) + c2 (-2+2)(x-3) + c3 (-2+2)(x-1)
-4 = c1 (-3)(-5)
-4/15 = c1

etc....

once the constants are known you can expand it into the quadratic to pull off a b and c

Answer 12

in the end ...(cough cough)... you can dbl check it with the wolf

http://www.wolframalpha.com/input/?i=interpolate+%28-2%2C-4%29%2C%281%2C-1%29%2C%283%2C-19%29

Answer 13

@amistre64 haha srry man im new didnt know that :P but u know explaining the way is just exhausting >.<

Answer 14

for this question, i totally agree :)