The vertex for of the equation of a parabola is x = ( y - 4 )2 + 27 what is the standard form

Important: indicate exponentiation with " ^ "

Thus, x = ( y - 4 )2 + 27 becomes x = ( y - 4 )^2 + 27

This can be re-written as x = y^2 - 8y + 16 + 27, or x = ay^2 - 8y + 43. This is the equation of the parabola in standard form x = ay^2 + by + c.

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emilianomatasperanza emilianomatasperanza · Answer 2 · 2019-07-22T18:33:57+02:00

Answer:

The standard form of this equation is

[tex] x = y^{2} - 8y + 43[/tex]

Step-by-step explanation:

The exercise is asking us to convert the given equation to the standard form. Our goal is to get an expression like the one below...

[tex] x = ay^{2} + by + c[/tex]

Now, let's work with the given parabola...

[tex] x = (y - 4)^{2} + 27[/tex]

We can apply the Square of the Binomial formula [tex] (a + b)^{2} = a^{2} + 2ab + b^{2}[/tex] to expand [tex](y - 4)^{2}[/tex]

Then, we get

[tex] x = y^{2} + 2y(-4) + (-4)^{2} + 27[/tex]

This can be simplified to

[tex] x = y^{2} - 8y + 16 + 27[/tex]

Finally, we can add number together

[tex] x = y^{2} - 8y + 43[/tex]