Final answer:
To rewrite the equation y = 2(x-1)² + 3 in the form y = ax² + bx + c, we need to multiply the perfect square trinomial by 2 and expand it. The final equation is y = 2x² - 4x + 5.
Step-by-step explanation:
To rewrite the equation y = 2(x-1)² + 3 in the form y = ax² + bx + c, we need to multiply the perfect square trinomial by 2. Let's start by expanding (x-1)²:
(x-1)² = (x-1)(x-1) = x² - 2x + 1
Now, multiply the perfect square trinomial by 2:
2(x² - 2x + 1) = 2x² - 4x + 2
Finally, add the constant term 3 to the result:
y = 2x² - 4x + 2 + 3
y = 2x² - 4x + 5