Question

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

Answer 1

A)
Because the greater the value if the co-efficient of x, the closer the graph is to the y axis ie: the narrower it is.

Answer 2

The graph of 2x^2 is narrowest .

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=
`2* 1=2`

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=
`(1)/(6) x^2`

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=
`(1)/(6)`

Put x=2 then we get

y=
`(2)/(3)`

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=
`-x^2`

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=
`(1)/(8) x^2`

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=
`(1)/(8)`

Put x= 2 then we get

y=
`(1)/(2)`

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.

Hence, we can see that quadratic equation y=2x^2 has narrowest graph.