Use the functions f(x) and g(x) to determine which function has the smallest zero and provide its coordinates.
f(x) = 3x2 + 18x − 21
x g(x)
18 −17
19 0
20 19
21 40
22 63
g(x); (19, 0)
g(x); (−17, 0)
f(x); (−7, 0)
f(x); (1, 0)

The smallest zero is (-7,0) and correspond to f(x)

Step-by-step explanation:

xg(x)    difference of g(x)   difference of differences

18−17

190         0 - (-17) = 17                          

2019        19  - 0 = 19                  19 - 17 = 2

2140       40 - 19 =21                 21 - 19 = 2

2263       63 - 40 =23              23 - 21 = 2

Then, g(x) is a quadratic function. The regression gives: g(x) = x^2 - 20x +19 (I made it in Excel, you can use any similar software or a calculator).

Using the quadratic formula, the zeros of g(x) are:

Coordinate of the zeros: (19, 0) and (1,0)

Using the quadratic formula, the zeros of f(x) are:

Coordinate of the zeros: (-7, 0) and (1,0)

yes.. it's proven to be 36.