Solve the inequality in terms of intervals and illustrate the solution set on the real number line. (x − 1)(x − 8) > 0
1 answer:
Answer:
The solution set of the given inequality is (-∞,1) ∪ (8,∞).
Step-by-step explanation:
The given inequality is
The related equation is
Two numbers 1 and 8 divide the number line in three intervals. (-∞,1), (1,8) ,(8,∞).
Intervals check point (x -1)(x -8) > 0 True or False
(-∞,1) 0 (-1)(-8)=8>0 True
(1,8) 2 (2-1)(2-8)=-6>0 False
(8,∞) 9 (9-1)(9-8)=8>0 True
The given inequality is true for (-∞,1) and (8,∞).
Therefore, the solution set of the given inequality is (-∞,1) ∪ (8,∞).
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ANSWER
(-3,3)
EXPLANATION
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where (h,k) =(-3,3) is the vertex
(-3,3)
EXPLANATION
The given function is
Expand
Rewrite in the form:
This implies that,
Complete the square to get,
The function is now in the form:
where (h,k) =(-3,3) is the vertex