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

Answer:

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

Step-by-step 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