y=-x^2 (-3<=x<=3)

Question

y equals x squared and then it has to the side -3 is less than or equal to x and x is less than or equal to 3

Answer 1

Hi Annie.  I assume we would like to determine what values of y satisfy this equation.  Let's substitute some possible values of x into the equation and solve for y.  

 

• x = 0, y=0
• x = 1, y=1
• x = 2, y=4
• x = 3, y=9

 

At the positive side of the spectrum, y ranges between 0 and 9.  Any value of x between 0 and 3 will have a value of y between 0 and 9.  

 

Now, let's say x is equal to a negative value, for example x=-1.  In this case, y is equal to 1.  Multiplying a negative number by a negative number yields a positive number.  What does this mean?  At the negative side of the spectrum, y ranges between 0 and 9 also.  

 

In conclusion, y ranges between 0 and 9, or 0 ≤ y ≥ 9.  

 

I hope this helps.  If not, feel free to write back!