Question

Which of the quadratic functions has the narrowest graph?

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

Answer:

The graph of 2x^2 is narrowest .

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=$2\times 1=2$

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=$\frac{1}{6} x^2$

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= $\frac{1}{6}$

Put x=2 then we get

y=$\frac{2}{3}$

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=$\frac{1}{8} x^2$

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=$\frac{1}{8}$

Put x= 2 then we get

y= $\frac{1}{2}$

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.