Question

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

Answer 1

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

Step-by-step 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= $( x^{2} - 6x+9) +36$
  = $x^{2} - 6x+45$