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nikitadnepr [17]
3 years ago
15

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 eq

uation of this parabola in standard form.
x= ( )^2 + ___
Mathematics
1 answer:
mario62 [17]3 years ago
4 0

Answer:

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

Step-by-step 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(\dfrac{coefficient\:of\:y}{2}\right)^{2}

Now coefficient of y is 8.

\therefore Last\:term\:of\:square=\left(\dfrac{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

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Answer:

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