Question

The vertex form of the equation of a parabola is y = (x - 3)2 + 36.

What is the standard form of the equation?

Answer 1

Answer:
`y=x^2-6x+45`

Explanation:

The equation of parabola in standard form is given by :-

`y=ax^2+bx+c`

Given : The vertex form of the equation of a parabola is
`y = (x - 3)^2 + 36.`

Using identity:

`(a-b)^2=a^2-2ab+b^2`

The above equation can be written as :

`y =x^2-2(3)x+(3)^2 +36\\\\\Rightarrow\ y=x^2-6x+9+36\\\\\Rightarrow\ y=x^2-6x+45`

Hence, the standard form of the equation =
`y=x^2-6x+45`

Answer 2

y=
`( x^(2) - 6x+9) +36`
=
`x^(2) - 6x+45`