Question

Each equation given below describes a parabola. Which statement best compares their graphs? X=2y^2 X=8y^2

A. Both parabolas open upward, and x=8y^2 is wider than x=2y^2.
B. Both parabolas open upwards, and x=2y^2 is wider than x=8y^2.
C. Both parabolas open to the right, and x=8y^2 is wider than x=2y^2.
D. Both parabolas open to the right, and x=2y^2 is wider than x=8y^2.

Answer 1

D)Both parabolas open to the right, and
`x=2y^2` is wider than
`x=8y^2.`

Explanation:

Standard equation of parabola :

`y=a(x-h)^2+k.`

If a < 0, then the parabola open downwards and if a > 0, then the parabola open upwards.

`x=a(y-k)^2+h`

If a < 0, then the parabola open left and if a > 0, then the parabola opens right

Given equations :
`X=2y^2` and
`X=8y^2`

`x=2(y-0)^2` and
`x=8(y-0)^2`

in both the equations a>0

So, Both parabolas are open to the right.

Refer the attached graph

`x=2y^2` ---- Red

`x=8y^2` --- blue

So,
`x=2y^2` is wider than
`x=8y^2.`

So, Option D is true