Find the quadratic function y=ax^2+bx+c using points...??pts: (-4,-9) (4,-9) and (5,-4) thank you!?

There are 3 unknowns in the function, a, b and c. If you plug in the 3 sets of values you will get 3 equations which you can use to solve the 3 unknowns.





1) -9 = 16a - 4b + c


2) -9 = 16a + 4b + c


3) -4 = 25a + 5b + c





subtract eqn 2) from eqn 1) to remove a and b, you get


0 = -8b


b = 0


plug b = 0 into eqn 2) and eqn 3) you get





3) -9 = 16a + c


4) -4 = 25a + c


subtract eqn 4) from eqn 3) to remove c


-5 = -9a


a = 5/9


from eqn 3) and a = 5/9


-9 = 16*5/9 + c


c = -9 - 80/9


c = -161/9





with a = 5/9, b = 0 and c = -161/9


the function y = ax^2 + bx + c becomes





y = 5/9x^2 - 161/9

Find the quadratic function y=ax^2+bx+c using points...??pts: (-4,-9) (4,-9) and (5,-4) thank you!?
just plug in the numbers,


I am not sure if x=-4 or -9, but that would be it.
Reply:since you know 3 points that this quadratic function pass through, then you can list three equations to solve for a,b,c 3 unknowns.





-9 = 16a - 4b +c


-9 = 16a +4b +c


-4 = 25a +5b +c





from here you can solve for a,b,c