what point is a solution to y=x3-2x

Question

 involving algebra 1. midterm review. what is the solution to the problem 

Answer 1

Hi Sarah--

 

You can find a solution by choosing a value for x and then applying the equation to it.

 

For example, say that x = 2.

 

2 to the third power, minus (2 times 2) = y

 

So, 8 - 4 = y, so y = 4 when x = 2

 

If you make x = 3, then x to the third power would be 27, then minus 2x would be minus 6, so

 

27 - 6 would be 21. So when x = 3, y = 21.

 

If you try a few different values for x, you'll see that the bigger you make x, the MUCH BIGGER y becomes, because bigger numbers raised to the 3rd power get HUGE in a hurry! (example, 10 to the 3rd is 1,000!)

 

Hope this helps!

 

Matt in NY

Answer 2

 

y = x³ - 2x       y = x(x² - 2)

 

Set both factors equal to zero:  x=0  and x² - 2 = 0

 

x² = 2    x = +/- √2

 

There are three solutions (x,y):   (-√2,0), (0,0), (+√2,0)