quadratic functions from widest to narrowest graph

Question

y=5x^2

y=x^2

y=0.75x^2

Answer 1

Hello Jessica! How are you?

To solve this question, you have to see first if all the functions have the same degree, which is the case, all have the degree of two. All equations have the shape of a parable.

A simple rule of thumb will be that the narrowest is the one with the biggest coefficient. The explanation goes as follows:

To get which is the widest and the narrowest, try compare then using simple values, for example:

For x = 0, we have

y = 0

y = 0

y = 0

For x = 2, we have:

y = 20

y = 4

y = 3

For x = - 2, we have:

y = 20

y = 4

y = 3

If you plot these graphs, you will see that the the first equation is the narrowest, and the third is the widest.