+0  
 
+3
310
2
avatar+253 

How do I find out the x and y intercepts when a graph is shown?

 

x^4+y^2-xy=16

sally1  Jun 12, 2014

Best Answer 

 #1
avatar+80815 
+8

This is certainly an unusual one, huh??    To find the x intercept, let's just let y=0

So we have x^4 = 16   →   x^4 - 16 = 0   ... which factors as

(x^2 - 4) (x^2 + 4) = 0    .... the second thing has a non-real solution but we can set the frist factor = 0  and find two real solutions

(x^2 - 4) = 0 .. factor as ..  (x+2) (x-2) = 0   so the x intercepts occur at (2,0) and (-2,0)

To find the y intercepts, let x = 0....so we have

y^2 = 16   →  y^2 - 16 = 0   factor this as ....  (y+4) (y-4) =0 and setting each factor to 0 produces y intercepts at  (0,4) and (0, -4)

I know that the "xy" term produces the graph of x^4 + y^2 = 16 with a "rotational" element added...heck, I'd even like to look at it myself !!!  (If I could add a stem at the top, it might resemble a strange "apple.')

Wow!!!.....that's certainly an odd duck!!...note that the intercepts are right where we said they would be, but as for the rest?? I couldn't begin to guess the shape of this one!!

CPhill  Jun 12, 2014
Sort: 

2+0 Answers

 #1
avatar+80815 
+8
Best Answer

This is certainly an unusual one, huh??    To find the x intercept, let's just let y=0

So we have x^4 = 16   →   x^4 - 16 = 0   ... which factors as

(x^2 - 4) (x^2 + 4) = 0    .... the second thing has a non-real solution but we can set the frist factor = 0  and find two real solutions

(x^2 - 4) = 0 .. factor as ..  (x+2) (x-2) = 0   so the x intercepts occur at (2,0) and (-2,0)

To find the y intercepts, let x = 0....so we have

y^2 = 16   →  y^2 - 16 = 0   factor this as ....  (y+4) (y-4) =0 and setting each factor to 0 produces y intercepts at  (0,4) and (0, -4)

I know that the "xy" term produces the graph of x^4 + y^2 = 16 with a "rotational" element added...heck, I'd even like to look at it myself !!!  (If I could add a stem at the top, it might resemble a strange "apple.')

Wow!!!.....that's certainly an odd duck!!...note that the intercepts are right where we said they would be, but as for the rest?? I couldn't begin to guess the shape of this one!!

CPhill  Jun 12, 2014
 #2
avatar+2353 
0

reinout-g  Jun 12, 2014

25 Online Users

avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details