Question

Chapter 3, Section 3.2, Question 017-018 For the function f (x) = a(x – r) (x – s) graphed below, state whether the constants a, r, and s are positive, negative, or zero. (Assume r < s.) a is ris s is 4. . . sis

Answer 1

the function is always positive

suppose x is tending to positive infinity

(x-r) would be positive

(x-s) would be positive

their product (x-r)(x-s) would also be positive

then for f(x) = a(x-r)(x-s) to be positive a must be positive

similarly you can check at negative infinity also if you want as (x-r)(x-s) would again be positive so a must be positive

a is positive

as f(x) is 0 on right side of y axis

means for some positive x f(x) is 0

so r or s both must bepositive

r is positive

s is positive

one more interesting thing to note is that this quadratic function f(x) touches x axis only once so both roots are equal also

so

r = s also holds