Question

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

Answer 1

The vertex form of the parabola is
`x=(y+5)^2-3`

C is the correct option.

Explanation:

The standard form of the parabola is
`x=y^2+10y+22`

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

For the expression
`y^2+10y`, the value of b is 10.

Hence, add and subtract
`((10)/(2))^2=25` to the right side of the equation.

Thus, the equation becomes

`x=y^2+10y+25-25+22`

Now, the expression
`y^2+10y+25=(y+5)^2`

Hence, we have

`x=(y+5)^2-25+22`

We can simplify further as

`x=(y+5)^2-3`

Hence, the vertex form of the parabola is
`x=(y+5)^2-3`

C is the correct option.

Answer 2

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.