Which of the quadratic functions has the narrowest graph?
a) y=2x^2
b) y= (1/6)x^2
c) y= -x^2
d) y=(1/8)x^2

Step-by-step explanation:

A).y=2x^2

When plot the graph for y=2x^2

The graph of y=2x^2 is parabola and along positive y-axis.The graph passing through origin .We can see

Put x=0 Then we get

 y=0

Hence, the parabola passing through origin.

When we put x=1 then we get

y=

Put x=2 we get

y=8

Put x=3  then we get

y=18

Hence, we can see as the value of x increases then the value of y increases  very sharply.

B).y=

The equation is also  a equation of parabola

The parabola along positive  y-axis.

Put x= 0 then we get

y=0

Hence, the parabola passing through the origin.

Put x=1 then we get

y=

Put x=2 then we get

y=

Put x= 3 then we get

y= 1.5

Hence, we can  when x increases then value of y  increases  slowly in comparison to x.

C). y=

The given equation is also a equation of parabola and along negative y- axis .

Putx=0 then we get

y=0

Hence, the parabola passing through the origin.

Put x=1 then we get

y= -1

Put x=2 then we get

y=-4

Put x=3 then we get

y=-9

Hence , value of y increases in direction of negtaive y-axis sharply  in comparison to x increases .

D). y=

The given equation is parabola and passing and along positive  y- axis .

Put x=0 then we get

y=0

Hence, the equation of parabola passing through the origin.

Put x=1 then we get

y=

Put x= 2 then we get

y=

Put x=3 then we get

y= 1.125

Hence , we can see that value of y increases very slowly in comparison to x increases.

d. 8

step-by-step explanation:

the given radical expression is:

we can rewrite this as:

we express as square numbers to get;

the exponents will now cancel out to give.

the correct answer is d

83-45=38

38 was the other number

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-thekoolkid1o1