Question 1171628: In the following equation a, b, and c are positive real numbers and a < b < c .
y=−(x+a)(x−b)^2 (x+c)
State the expression, in terms of a, b and c, that represents the y-intercept.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
The y intercept always occurs when x = 0
Plug in x = 0 to get,
y = -(x+a)*(x-b)^2*(x+c)
y = -(0+a)*(0-b)^2*(0+c)
y = -(a)*(-b)^2*(c)
y = -a*b^2*c
The y intercept is -a*b^2*c
The location of the y intercept as an (x,y) point is (0, -a*b^2*c)
Since a,b,c are positive this makes a*b^2*c to be positive as well.
This flips to -a*b^2*c being negative.
Visually this indicates the function curve crosses the y axis somewhere below the x axis.
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Answer: The y intercept is -a*b^2*c and it's some negative number.
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