how will the graph of the function y=x^2 be affected if the coefficient of x^2 is decreased to 1/2?

Question

graph decrease

Answer 1

The basic parabola y = x² will be 'flattened' by having the coefficient ½ applied to its definition.  That is, every y value will be half of its former value. This is often called a vertical compression. Only one point, its vertex, is unchanged because (0,0) half of zero is still zero, so the vertex stays put at the origin.

Answer 2

let's make a table of x^2 :

 

x    |   y

-2   |   (-2)^2 = 4

-1   |   (-1)^2 = 1

0    |    (0)^2 = 0

1    |   (1)^2 = 1

2    |   (2)^2 = 4

 

 

let's make a table of (1/2) * x^2 :

x | y
-2 | (1/2) * (-2)^2 = 2
-1 | (1/2) * (-1)^2 = 1/2
0 | (1/2) * (0)^2 = 0
1 | (1/2) * (1)^2 = 1/2
2 | (1/2) * (2)^2 = 2

try to graph them now. can you see what happened after we multiplied with (1/2). it got compressed VERTICALLY.

 

 

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