Question 946075: What is a sign graph and when is it used? Give an example. Explain what the test-point method is and how it is used to solve a quadratic inequality. Be sure to show the connection between the test-point method and a sign graph. (I am completely lost Please Help!)
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! 1)If we can factor a quadratic inequality, then the inequality can be solved with a sign graph, which shows where each factor is positive, negative, or zero.
for example,
x^2 +3x -10 > 0
factor polynomial
(x+5)*(x-2) > 0
This inequality says that the product of x + 5 and x - 2 is positive. If both factors are negative or both are positive, the product is positive. To analyze the signs of each factor, we make a sign graph. First consider the possible values of the factor x + 5
x+5=0 if x=-5 put 0 above -5 on number line
x+5>0 if x>-5 put + to the right of -5
x+5<0 if x<-5 put - to the left of -5
now do the same analysis for x-2=0, x-2>0, x-2<0
2) First determine zeros for the polynomial in 1
(x+5)*(x-2) = 0 and
zeros are -5 and 2
To solve by the Test-Point Method, pick a sample point in each interval, the intervals being (negative infinity, –5), (-5, 2), (2, positive infinity)
remember that our inequality from 1 is
x^2 +3x -10 > 0
evaluate the inequality for each test point and
(note that we are interested in the interval/s that give us a positive value)
If the rational expression is greater than 0, then we are interested in values that cause our rational expression to be positive.
3) both methods use the sign of evaluated expressions to find the solution set.
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