Question

The function y=-5(x-4)² +10 shows the daily profit (in hundreds ofdollars) of a taco food truck, where x is the price of a taco (in dollars). Findand interpret the zeros of this function.Select two answers: one for the zeros and one for the interpretation.A. Interpretation: The zeros are where the daily profit is $0.00.B. Zeros: x=4-√2=2.58 and x = 4+ √2 = 5.41C. Zeros: x= 4 and x = -4D. Interpretation: The zeros are where the price of a taco is $0.00.

Answer 1

To answer this question we will set y=0 and then solve for x.

Setting y=0 we get:

$0=-5(x-4)^2+10.$

Adding 5(x-4)² to the above result we get:

$\begin{gathered} 0+5(x-4)^2=-5(x-4)^2+10+5(x-4)^2, \\ 5(x-4)^2=10. \end{gathered}$

Dividing the above result by 5 we get:

$\begin{gathered} \frac{5(x-4)^2}{5}=\frac{10}{5}, \\ (x-4)^2=2. \end{gathered}$

Therefore:

$x-4=\pm\sqrt2.$

Adding 4 to the above result we get:

$\begin{gathered} x-4+4=\pm\sqrt2+4, \\ x=4\pm\sqrt2. \end{gathered}$

Since y represents the daily profit in hundreds of dollars, then the zeros are where the daily profit is $0.00.

Answer: Options A and B.