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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 + ___

2 Answers

4 votes

Answer:

this is the correct answer:

Explanation:

The equation y^2+8y−x+18=0 represents a parabola. Drag and drop the expressions into-example-1
User Gavin Portwood
by
5.9k points
5 votes

Answer:

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

User Alberto Morillo
by
7.2k points
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