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

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MrGumby

Answer:

The correct answer is D. Both parabolas open to the right, and x=2y^2 is wider than x=8y^2

Step-by-step explanation:

We can tell this since it is an x = equation, then it must open to the right of left. Since they are both positive, it would be the right.

Secondly, as the coefficient gets higher, the lines get steeper. Therefore, we know that 8 is steeper than 2 and is less wide.

presipao

Answer:

C. Both parabolas open to the right, and, [tex]x=8y^2[/tex] is wider than [tex]x=2y^2[/tex]

Step-by-step explanation:

The general equation of a parabola that opens horizontally is

[tex]x=4ay^2[/tex]

which is exactly our case. Moreover, if [tex]a>0[/tex] it opens to the right, and if [tex]a<0[/tex] it opens to the left. In our case, it holds for the first parabola that

[tex]4a=2\quad\Rightarrow\quad a=\dfrac{1}{2}[/tex]

and for the second one

[tex]4a=8 \quad\Rightarrow\quad a=4[/tex]

hence in both cases [tex]a>0[/tex] and so both parabolas open to the right.

To see which one is wider let us evaluate x at y=1, for the first parabola we have

[tex]x(y=1)=2\cdot(1)^2=2[/tex]

and

[tex]x(y=1)=8\cdot(1)^1=8[/tex]

in general we have [tex]8y^2>2y^2[/tex] for [tex]y\neq0[/tex] , and so we can see that the second parabola is wider than the first one.

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