Question 1087736
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:


<img src = "http://theo.x10hosting.com/2017/071501.jpg" alt="$$$" </>


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