Label Corner Points

Nov 2019
13
2
NYC
Label corner points given the system of nonlinear inequalities. MathMagic191105_2.png
 

topsquark

Forum Staff
Jan 2006
11,552
3,443
Wellsville, NY
By "corner points" I presume you are looking for intersection points on the boundary of the solution? These can be found by solving the simultaneous equations
\(\displaystyle x^2 - y = 0\)
\(\displaystyle 2x^2 + y = 12\)

So the first equation has the solution \(\displaystyle y = x^2\). Put that into the second equation and solve for x. Can you finish?

-Dan
 
Mar 2012
558
29
if you draw the two inequalities, you will see clearly where the corners are. you have to find the bounded area and then look for any intersections around it. to find any intersecting lines, first convert the inequalities to equal signs (=), then solve for y for both

y = x^2
y = 12 - 2x^2

then make them equal and solve for x

x^2 = 12 - 2x^2

here is a picture of the corners

DC91B731-3AE3-4018-BD8F-7D238C0232C9.jpeg
 
Nov 2019
13
2
NYC
By "corner points" I presume you are looking for intersection points on the boundary of the solution? These can be found by solving the simultaneous equations
\(\displaystyle x^2 - y = 0\)
\(\displaystyle 2x^2 + y = 12\)

So the first equation has the solution \(\displaystyle y = x^2\). Put that into the second equation and solve for x. Can you finish?

-Dan
Dan,

I can do it now. However, member joshuaa was nice enough to provide a complete solution and graph.
 
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Reactions: joshuaa
Nov 2019
13
2
NYC
if you draw the two inequalities, you will see clearly where the corners are. you have to find the bounded area and then look for any intersections around it. to find any intersecting lines, first convert the inequalities to equal signs (=), then solve for y for both

y = x^2
y = 12 - 2x^2

then make them equal and solve for x

x^2 = 12 - 2x^2

here is a picture of the corners

View attachment 39568
Nice reply and picture, too. Desmos, right?
 
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Reactions: joshuaa
Mar 2012
558
29
Yes, Desmos. It is a great website to graph your functions!
 
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Reactions: xyz_1965