Question 9(Multiple Choice Worth 1 points) (08.05 MC) Use the functions f(x) and g(x) to determine which function has the smallest zero and provide its coordinates. f(x) = 2x2 − 14x + 20 x g(x) 18 −17 19 0 20 19 21 40 22 63 f(x); (2, 0) f(x); (−5, 0) g(x); (19, 0) g(x); (−17, 0)
Answers
Given:
f(x) = 2x2 − 14x + 20 x g(x) 18 −17 19 0 20 19 21 40 22 63 f(x); (2, 0) f(x); (−5, 0) g(x); (19, 0) g(x); (−17, 0)
To find:
Use the functions f(x) and g(x) to determine which function has the smallest zero and provide its coordinates.
Solution:
From given, we have,
x g(x) difference of g(x) difference
18 −17
19 0 0 - (-17) = 17
20 19 19 - 0 = 19 19 - 17 = 2
21 40 40 - 19 =21 21 - 19 = 2
22 63 63 - 40 =23 23 - 21 = 2
Thus g(x) is a quadratic function and the regression is given as,
g(x) = x^2 - 20x + 19
The zeros of g(x) are given by,
x = ±√[(-20)² - 4(1)(19)]/2(1)
x = ±9
The coordinates of zeros are (-9, 0) and (9, 0)
f(x) = 2x^2 − 14x + 20
The zeros of f(x) are given by,
x = ±√[(-14)² - 4(2)(20)]/2(2)
x = ± 1.5
The coordinates of zeros are (-1.5, 0) and (1.5, 0)
The smallest zero is (-1.5, 0) and it corresponds to f(x).
Answer:
c.
Step-by-step explanation: