quadratic function

Question

Find a quadratic function y=ax^2+bx+c whose graph passes through the points (1,3),(3,-1) ans (4,0).

 

Show work please

Answer 1

Plug in the (x,y) values given:

(1) 3=a+b+c

(2) -1=9a+3b+c

(3) 0=16a+4b+c

We have 3 equations and 3 unknowns, so we have a potential solution.

(4): (2)-(1): -4=8a+2b

(3)-(2): 1=7a+b, so b=1-7a. Substitute for b in (4): -4=8a+2-14a=-6a+2; 6a=6, a=1, so b=1-7=-6 and c=3-(a+b)=8.

So y=x^2-6x+8.