Question 1087736: Solve the quadratic inequality. Write the solution set in interval notation.Please show your complete step by step solution.
y^2-17y+70<0
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! set it equal to 0 and factor.
you get y^2 - 17y + 70 = 0 becomes (y - 7) * (y - 10) = 0
set each factor to 0 and you get:
y - 7 = 0
y - 10 = 0
solve for y and you get:
y = 7
y = 10
the value of the equation is equal to 0 when y = 7 and y = 10
look for the area where:
y < 7
y > 10
y > 7 and < 10 which can be shown as 7 < y < 10
pick any values of y in those areas.
i chose y = 5, y = 15, y = 8
when y = 5, the equation = 10 which is positive.
when y = 15, the equation = 40 which is positive.
when y = 8, the equation = -2 which is negative.
since the equation is continuous, it will remain negative until it crosses a zero point at which time it will remain positive until it reaches another zero point, and vice versa.
therefore y > 0 when y < 7 and y > 10, and y < 0 when 7 < y < 10.
in interval notation, this would look like this:
equation is greater than 0 when y = (minus infinity,7) union (10, plus infinity)
this translates to the value of y is between minus infinity and 7, or between 10 and plus infinity, but does not include 7, 10, or infinity (plus or minus).
equation is less than 0 when y = (7,10)
this translates to the value of y is between 7 and 10, but does not include 7 or 10.
equation is equal to 0 when y = [7,7] union [10,10]
this translates to the value of y is equal to 7 or equal to 10.
graphically, the equation would look like this:
the y-axis is at x = 0
the x-axis is at y = 0
the coordinates are shown as (x,y)
for example, (40,15) means that the value of x is 40 when the value of y is 15.
x represents the value of the equation.
for example, (40,15) means that the value of the equation is 40 when the value of y is 15.
the equation used for graphing is x = y^2 - 17x + 70
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