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

x = √2 + 2, -√2 + 2

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 =
`(-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 +/- √(2)`

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

`√(2) = (√(x-2) )^(2)`

+/-
`√(2)` = x - 2

+2 +2

`2 +/- √(2)` = x