The function y= -6(x - 5)2 + 12 shows the daily profit (in hundreds of dollars) of a taco food truck, where x is the price of a taco (in dollars). Find and interpret the zeros of this function. Select two answers: one for the zeros and one for the interpretation. O A. Interpretation: The zeros are where the price of a taco is $0.00. B. Zeros: * = 5 – /2 - 3.58 and x = 5+2=6.41 I c. Zeros: x= 5 and x = -5 O D. Interpretation: The zeros are where the daily profit is $0.00

To find the zeros of the function y = -6(x - 5)² + 12, we need to set y equal to zero and solve for x:

0 = -6(x - 5)² + 12

Firstly, move the 12 to the other side:

-6(x - 5)² = -12

Now divide by -6:

(x - 5)² = 2

Next, take the square root of both sides to solve for x:

√(x - 5)² = ±√2

x - 5 = ±√2

Now solve for x by adding 5 to both sides:

x = 5 ± √2

Therefore, the zeros of the function are:

x = 5 + √2 x = 5 - √2

And the approximate values for the zeros are:

x ≈ 5 + 1.41 = 6.41 x ≈ 5 - 1.41 = 3.59

Hence the correct choice for the zeros is:

B. Zeros: x = 5 - √2 ≈ 3.59 and x = 5 + √2 ≈ 6.41

For the interpretation part, zeros of the function represent the values of x for which the daily profit (y) is zero. Since y represents the profit in hundreds of dollars, the correct interpretation is that the zeros are the prices at which the profit will be $0.00. Hence, the answer is:

D. Interpretation: The zeros are where the daily profit is $0.00