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Luv2Teach
A sideways opening parabola is in the form [tex]x= y^{2} [/tex], so we know from the process of elimination that it will either be b or c.  Next we have to realize that if the parabola opens to the left it is a negative parabola, just like if a parabola opens upside down it is a negative parabola.  So the one that has the negative out front is b. 

Answer:

Option b - [tex]x=-3(y-2)^2-17[/tex]

Step-by-step explanation:

Given : A parabola that opens to the left with vertex (-17,2).

To find : Which of the following could be the equation for a parabola?

Solution :

The general form of the parabola that opens to the left i.e. horizontal is given by :

[tex]x=a(y-k)^2+h[/tex]

Where, (h,k) are the vertex of the parabola

and a is negative because parabola opens left.

We have given the vertex (-17,2)=(h,k)

The rough equation of the parabola is [tex]x=a(y-2)^2-17[/tex]

The only option matches with our equation is option b.

Therefore, The required form of the parabola is [tex]x=-3(y-2)^2-17[/tex]

So, Option b is correct.

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