To convert the equation from vertex form \( y = -2(x-3)^2 + 1 \) to standard form, we need to expand the equation.
-
Start with the given vertex form: \[ y = -2(x - 3)^2 + 1 \]
-
Expand \((x - 3)^2\): \[ (x - 3)(x - 3) = x^2 - 6x + 9 \]
-
Substitute this back into the equation: \[ y = -2(x^2 - 6x + 9) + 1 \]
-
Distribute \(-2\) across the terms: \[ y = -2x^2 + 12x - 18 + 1 \]
-
Combine the constant terms: \[ y = -2x^2 + 12x - 17 \]
So the standard form of the equation is: \[ y = -2x^2 + 12x - 17 \]
The correct answer is: b. \( y = -2x^2 + 12x - 17 \).