Question

The function y = -2(x - 2) + 6 shows the daily
profit (in hundreds of dollars) of a hot dog stand, where x is the price of a hot dog (in dollars). Find and interpret the zeros of this function.
Select two answers: one for the zeros and one for the interpretation.
O The zeros are the hot dog prices that give
$0.00 profit (no profit).
• Zeros at x = 2 and x = 6
O Zeros at x = 2 ÷ V3
O The zeros are the hot dog prices at which
they sell 0 hot dogs.

Answer 1

To find the zeros of the function \( y = -2(x - 2) + 6 \), we set \( y = 0 \) and solve for \( x \).

1. Set the equation equal to zero:
\[
0 = -2(x - 2) + 6
\]

2. Rearranging gives:
\[
-2(x - 2) = -6
\]

3. Dividing both sides by -2:
\[
x - 2 = 3
\]

4. Solving for \( x \):
\[
x = 5
\]

So, the zero of the function occurs at \( x = 5 \).

### Interpretation
The zeros represent the hot dog prices at which the profit is $0.00 (no profit).

### Answers:
- Zeros: At \( x = 5 \)
- Interpretation: The zeros are the hot dog prices that give $0.00 profit (no profit).

The correct answers from your options are:
- Zeros at x = 5
- The zeros are the hot dog prices that give $0.00 profit (no profit).