Question

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

Answer 1

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.

Answer 2

Answer:

The standard form of this equation is

$x = y^{2} - 8y + 43$

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...

$x = ay^{2} + by + c$

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

$x = (y - 4)^{2} + 27$

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

Then, we get

$x = y^{2} + 2y(-4) + (-4)^{2} + 27$

This can be simplified to

$x = y^{2} - 8y + 16 + 27$

Finally, we can add number together

$x = y^{2} - 8y + 43$