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11.2.3 Quiz: Completing the Square

Question 1 of 10

2 Points


The function y = -2(x- 3)2 + 4 shows the daily profit (in hundreds of dollars)

of a hot dog stand, where x is the price of a hot dog (in dollars). Find and

interpret the zeros of this function.

Select two answers: one for the zeros and one for the interpretation.


A. Zeros at x - 34 /2

B. The zeros are the hot dog prices that give $0.00 profit (no profit)

C. Zeros at x = 2 and x = 3

D. The zeros are the hot dog prices at which they sell 0 hot dogs.

Respuesta :

MrRoyal

Answer:

A. The zeros is at: [tex]3 \±\sqrt 2[/tex]

B. The zeros are the hot dog prices that give $0.00 profit (no profit)

Step-by-step explanation:

Given

[tex]y = -2(x - 3)^2 + 4[/tex]

Solving (a): The zeros of the function

To do this, we equate y to 0.

[tex]y = 0[/tex]

So, we have:

[tex]-2(x - 3)^2 + 4 =0[/tex]

Subtract 4 from both sides

[tex]-2(x - 3)^2 + 4 -4=0 -4[/tex]

[tex]-2(x - 3)^2 = -4[/tex]

Divide both sides by -2

[tex](x - 3)^2 = 2[/tex]

Take the square root of both sides

[tex](x - 3) = \sqrt 2[/tex]

Add 3 to both sides

[tex]x =3 \±\sqrt 2[/tex]

Option (b) interprets the zeros

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