Can some one help me with a functions question?

Question

Find the numbers a,b and c if the graph of the function f(x) = ax^2+bx+c passes through the points (0, -3), (1,3) and (-2,-3)

can someone please explain how to do this question? any help would be great.

Answer 1

insert the corordinate values (x,y) into the function for each co-ordinate pair.

Thus we get:

c=-3

a+b+c=3

4a-2b+c=-3

so if we use the first equation and substitue it into the other 2 we get:

a+b-3=3

4a-2b-3=-3

or a+b=6 and 4a-2b=0

this is a pair of simultaneous equations which you can solve by the usual method to obtain a & b

e.g. divide the 2nd equation by 2 to give 2a-b=0

add the 1st equation to the 2nd to obtain 3a=6 so a=2 so therefore b=4

Hence I reckon that a=2, b=4 and c=-3

Answer 2

Simple, plug in the given pairs of x,y values

and you get three simultaneous equations in a, b, c

which you then solve.

The 1st point gives you  -3 = 0 + 0 + c      so c= -3

you can do the rest!