Answer:
D. The zeros are the hot dog prices that give $0.00 profit (no profit).
Step-by-step explanation:
Given the function y=-2(x-3)² + 4
The zeros of the function are the points at which the graph of the function crosses the x axis if plotted. y is the daily profit (in hundreds of dollars) and x is the price of the hot dog. To find the zeros, we substitute x = 0 and solve.
Therefore: y=2(x-3)² + 4
0 = 2(x-3)² + 4
-2(x² - 6x + 9) + 4 = 0
-2x² + 12x - 18 + 4 = 0
2x² - 12x + 18 - 4 = 0
2x² - 12x + 14 = 0
2(x² - 6x + 7) = 0
x² - 6x + 7 = 0
Solving the quadratic equation gives:
x = 3 + √2 and x = 3 - √2
This means that the graph crosses x at 3 + √2 and 3 - √2.
The zeros of the function are 3 + √2 and 3 - √2. The zeros of the function is the point where y = 0, that is the point that the hot dog prices that give $0.00 profit (no profit).
