Respuesta :

calculista

we know that

The parabola shown on the graph represent a vertical parabola open upward with vertex at the origin

so

the equation of the parabola is equal to

[tex]x^{2}=4ay[/tex] ------> equation A

the equation of the directrix is equal to

[tex]y=-a[/tex]

In this problem we have

the equation of the directrix is equal to

[tex]y=-1.5[/tex]

so

the value of a is equal to

[tex]a=1.5[/tex]

substitute the value of a in the equation A

[tex]x^{2}=4(1.5)y[/tex]

[tex]x^{2}=6y[/tex]

therefore

the answer is the option

[tex]x^{2} =6y[/tex]

The equation that represents the parabola shown on the graph is x^2=4y.

We have given the equations

y^2 = 1.5x

x^2 = 1.5y

y^2 = 6x

x^2 = 6y

What is the parabola?

The parabola shown on the graph represents  a vertical parabola open upward with a vertex at the origin

The equation of the parabola is equal to

x^2=4ay equation A

The equation of the directrix is equal to

y=-a

In this problem we have

The equation of the directrix is equal to

y=-1.5

So, the value of a is equal to

a=1.5

Substitute the value of a  in  equation A

x^2=4(1.5)y

x^2=6y

Therefore, The answers are the option x^2=4y.

To learn more about the parabola visit:

https://brainly.com/question/4148030

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