Convert the equation `y=-2\left(x-3\right)^{2}+1` from vertex form to standard form.

Question

a. y=2x^{2}-9x-17
b. y=-2x^{2}+12x-17
c. y=-2x^{2}-19x-1
d. y=2x^{2}+2x-9

Answer 1

To convert the equation from vertex form \( y = -2(x-3)^2 + 1 \) to standard form, we need to expand the equation.

1. Start with the given vertex form: \[ y = -2(x - 3)^2 + 1 \]

2. Expand \((x - 3)^2\): \[ (x - 3)(x - 3) = x^2 - 6x + 9 \]

3. Substitute this back into the equation: \[ y = -2(x^2 - 6x + 9) + 1 \]

4. Distribute \(-2\) across the terms: \[ y = -2x^2 + 12x - 18 + 1 \]

5. 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. \( y = -2x^2 + 12x - 17 \).