Question

A quadratic function is a function of the form y=ax2+bx+c where a, b, and c are constants. Given any 3 points in the plane, there is exactly one quadratic function whose graph contains these points.

Find the quadratic function whose graph contains the points (0,3), (2,15), and (−1,0).

Answer 1

distribute all point into y=ax2+bx+c, we have 3 equations :

((),3) --> 3 = a(0)^2 + b(0) + c, or
c = 3 ... (1)

(2,15) --> 15 = a(2)^2 + b(2) + c = 15 or
15 = 4a + 2b + c
beause c = 3, therefore the equa above can be
15 = 4a + 2b + 3 or
4a + 2b = 12
(divide by 2)
2a + b = 6 ... (2)

(-1,0) --> 0 = a(-1)^2 + b(-1) + c
0 = a - b + c
again, subtitute c = 3 we get
a - b + 3 = 0
a - b = -3 ... (3)

by using elimination and subtitution method, solve for a and b for both equations (2 and 3)

2a + b = 6
a - b = -3
(solve for a and b)
continue it ...

Answer 2

ohhh ok. thank you!