Question

the profit for a taco truck business follows this function, where x is the price of a taco(in dollars) and y is the daily profit(in hundreds of dollars):y=-2(x-2)^2+4. find and interpret the zeros of this function. HINT: replace y with 0 and solve for x

Answer 1

Answer:

x = √2 + 2, -√2 + 2

Step-by-step explanation:

y = -2(x-2)² + 4

-2(x-2)² + 4 = 0 --- replace y with 0

-2(x - 2)² = -4 --- subtract 4 from both sides

(x - 2)² = $\frac{-4}{-2}$ --- divide both sides by -2

(x - 2)² = 2 --- simplify

x - 2 = +-√2 --- square root both sides

x - 2 = √2 --- split into 2 equations

x - 2 = -√2

x = √2 + 2 --- solve first equation

x = -√2 + 2 --- solve second equation

x = √2 + 2, -√2 + 2

Answer 2

Answer: $2 +/- \sqrt{2}$

Step-by-step explanation:

 y = -2(x - 2)² + 4

 0 = -2(x - 2)² + 4

÷-2   ÷-2          ÷-2

 0  = (x - 2)² - 2

+2                +2

 2  = (x - 2)²

$\sqrt{2} = (\sqrt{x-2} )^{2}$

+/- $\sqrt{2}$ = x - 2

+2              +2  

$2 +/- \sqrt{2}$ = x