Fabio is designing a flashlight that uses a parabolic reflecting mirror and a light source. The shape of the mirror can be modeled by (x-2)^2=10(y-3), where x and y are measured in inches. Where is the focus of the flashlight?

F(2, 11/2)

Step-by-step explanation:

The expression:

(x-2)² = 10(y - 3)

can be rewritten in the vertex form as follows:

(x-2)² = 10y - 30

(x-2)² + 30 = 10y

1/10(x-2)² + 3 = y

General vertex form is:

y = a(x-h)² + k

then, the vertex is locate at (h, k). In this case the vertes is (2, 3), and a = 1/10

The focus of a parabola is located ar F(h, k+p), where p = 1/(4a). Replacing into these equations:

p = 1/(4*1/10) = 5/2

F(2, 3+5/2) = F(2, 11/2)

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!

the answer is (-4,-4)

hope this ! : d