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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

Respuesta :

professorlopes001
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.
Ver imagen professorlopes001

Answer:

C. [tex]y = \frac{1}{4}x^2, y = -\frac{1}{2}x^2, y = \frac{3}{2}x^2[/tex]

Step-by-step 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,

[tex]y = \frac{1}{4}x^2, y = -\frac{1}{2}x^2, y = \frac{3}{2}x^2[/tex]

Since,

[tex]|\frac{3}{2} > |-\frac{1}{2}| > |\frac{1}{4}|[/tex]

Hence, by the above statement,

The order of parabolas from widest to narrowest,

[tex]y = \frac{1}{4}x^2, y = -\frac{1}{2}x^2, y = \frac{3}{2}x^2[/tex]

Option 'C' is correct.

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