Question

The equation y^2+8y−x+18=0 represents a parabola. Drag and drop the expressions into the boxes in the equation to rewrite the equation of this parabola in standard form.

x= ( )^2 + ___

Answer 1

this is the correct answer:

Explanation:

Answer 2

The equation of parabola is standard form is
`x=\left(y+4\right)^2+2`

Explanation:

Given equation of parabola is,

`y^2+8y-x+18=0`

In order to find the equation of parabola in standard form, eliminate x from left side of equation and use completing square method to find the equation.

First step is to add x on both side of equation.

`y^2+8y-x+18+x=0+x`

`y^2+8y+18=x`

Rewriting,

`x=y^2+8y+18`

Now applying completing square method as follows.

Following are the steps for calculation of this method.

Find the last term of above equation by using below formula,

`Last\:term\:of\:square=\left((coefficient\:of\:y)/(2)\right)^(2)`

Now coefficient of y is 8.

`\therefore Last\:term\:of\:square=\left((8)/(2)\right)^(2)`

Simplifying,

`Last\:term\:of\:square=\left(4\right)^(2)`

`Last\:term\:of\:square=16`

Second step is to add and subtract the last term.

`x=y^2+8y+18+16-16`

Rewriting,

`x=y^2+8y+16+18-16`

Since
`\left(a+b\right)^(2)=a^(2)+2ab+b^(2)`

Using above formula,

`x=\left(y+4\right)^(2)+2`

Therefore, the equation of parabola in standard form is
`x=\left(y+4\right)^(2)+2`