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joemama69
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Homework Statement
Sketch the graph of the function f(x,y) = 1 - y^2
Homework Equations
The Attempt at a Solution
see pic
The graph of f(x,y) = 1 - y^2 is a parabola that opens downwards along the y-axis. It is a symmetrical curve that extends infinitely in both the positive and negative x-directions.
Changing the value of x will shift the parabola horizontally, but the shape will remain the same. A larger x-value will result in a rightward shift, while a smaller x-value will result in a leftward shift.
As the value of y increases, the parabola will shift downwards along the y-axis. This results in a narrower shape as the curve approaches the x-axis.
The vertex of the graph can be found by setting y = 0 and solving for x. In this case, the vertex is at (0,1).
Yes, the graph is symmetrical along the y-axis. This means that if you were to fold the graph in half along the y-axis, the two halves would match up perfectly.