Answered

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

Verified Answer :

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.

View image professorlopes001

Answer:

C. \(y = \frac{1}{4}x^2, y = -\frac{1}{2}x^2, y = \frac{3}{2}x^2\)

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,

\(y = \frac{1}{4}x^2, y = -\frac{1}{2}x^2, y = \frac{3}{2}x^2\)

Since,

\(|\frac{3}{2} > |-\frac{1}{2}| > |\frac{1}{4}|\)

Hence, by the above statement,

The order of parabolas from widest to narrowest,

\(y = \frac{1}{4}x^2, y = -\frac{1}{2}x^2, y = \frac{3}{2}x^2\)

Option 'C' is correct.

Related Questions