How can I order the following functions from narrowest to widest

Question

f(x)=3/4x^2; g(x)=-2x^2; hf(x)=-8x^2; j(x)=1/2x^2;k(x)=-1/8x^2

Answer 1

Hello, for this problem, positives and negatives do not matter, as they only affect the parabola opening up or down. We simply need to look at the "a" values or the coefficients listed in front of each x².

The larger the a value, the narrower the parabola. The smaller the a value, the wider the parabola.

Here are you a values.

3/4

-2

-8

1/2

-1/8

Forgetting about negatives, the largest value here is 8, then 2. Continuing from there, we get:

8, 2, 3/4, 1/2, 1/8

This orders the parabolas from narrowest to widest, as shown below:

h(x) = -8x², g(x)= -2x², f(x) = 3/4x², j(x) = 1/2x², i(x) = 1/8x²