can someone help me please!

Question

A student thinks that y= 2x^2 - 12x + 15 is equivalent to y= 2( x-3)^2 + 3. prove algebraically that they are not equivalent.

Answer 1

First equation : y₁ = 2x² - 12x + 15

Second equation : y₂ = 2(x-3)² + 3

Apply formula : (a-b)²=a²-2ab+b²

y₂ = 2( x² - 2(x)(3) - 3² ) + 3

y₂ = 2( x² - 6x - 9 ) + 3

y₂ = 2x² - 12x - 18 + 3

y₂ = 2x² - 12x - 15

y₂ is not equals to y₁

Solution :

First equation (y₁ = 2x² - 12x + 15) and Second equation (y₂ = 2(x-3)² + 3) algebraically that they are not equivalent