Question

Order the group of parabolas from widest to narrowest

y = 1/4x 2, y = -1/2x 2, y = 3/2x 2

Which option would it be?

A.
y = 1/4x 2, y = 3/2x 2, y = -1/2x 2

B.
y = -1/2x 2, y = 1/4x 2, y = 3/2x 2

C.
y = 1/4x 2, y = -1/2x 2, y = 3/2x 2

D.
y = 3/2x 2, y = -1/2x 2, y = 1/4x 2

Answer 1

How bigger is "x" coefficient, widest is the parabola, independent if this coefficient is positive ou negative. I atacched an image to illustrate. The correct is alternative "C". Thanks.

Answer 2

C.
`y = (1)/(4)x^2, y = -(1)/(2)x^2, y = (3)/(2)x^2`

Explanation:

Since, the upward or downward parabola with the least absolute value of coefficient of x² is widest while with the largest absolute value of coefficient of x² is narrowest,

Here, the given upward and downward parabolas,

`y = (1)/(4)x^2, y = -(1)/(2)x^2, y = (3)/(2)x^2`

Since,

`|(3)/(2) > |-(1)/(2)| > |(1)/(4)|`

Hence, by the above statement,

The order of parabolas from widest to narrowest,

`y = (1)/(4)x^2, y = -(1)/(2)x^2, y = (3)/(2)x^2`

Option 'C' is correct.