The standard form of the equation of a parabola is x = y2 + 10y + 22. What is the vertex form of the equation?

I think the correct answer from the choices listed above is option C. The vertex for of the equation x = y2 + 10y + 22 would be x = (y-5)^2 - 3 where the vertex is at (5, -3). The vertex form of a parabola is expressed as x = a(x - h)^2 + k where h,k is the vertex. Hope this answers the question.

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SociometricStar SociometricStar · Answer 2 · 2019-03-19T11:43:03+01:00

Answer:

The vertex form of the parabola is [tex]x=(y+5)^2-3[/tex]

C is the correct option.

Step-by-step explanation:

The standard form of the parabola is [tex]x=y^2+10y+22[/tex]

We can write this equation in vertex form by using the completing square method.

For the expression [tex]y^2+10y[/tex], the value of b is 10.

Hence, add and subtract [tex](\frac{10}{2})^2=25[/tex] to the right side of the equation.

Thus, the equation becomes

[tex]x=y^2+10y+25-25+22[/tex]

Now, the expression [tex]y^2+10y+25=(y+5)^2[/tex]

Hence, we have

[tex]x=(y+5)^2-25+22[/tex]

We can simplify further as

[tex]x=(y+5)^2-3[/tex]

Hence, the vertex form of the parabola is [tex]x=(y+5)^2-3[/tex]

C is the correct option.