Please help ! Math
-

f(x) = 2(x - 2)^2 - 1

vertex: (2, -1)

Step-by-step explanation:

f(x) = 2x^2 - 8x + 7

First, we find the vertex.

x = -(-8)/4 = 2

y = 2(2)^2 - 8(2) + 7 = 2(4) - 16 + 7 = 8 - 9 = -1

vertex: (2, -1)

Second, we write f(x) in vertex form.

we know that h and k have to be 2 and -1.

2x^2 - 8x + 7 = a(x - 2)^2 - 1

Since 8 - 1 = 7, we do this:

f(x) = (2x^2 - 8x + 8) - 1

Factor out the 2 and then factor the polynomial

f(x) = 2(x^2 - 4x + 4) - 1

factors of 4:

1 4

2 2

-1 -4

-2 -2 = -4

the function in vertex for is:

f(x) = 2(x - 2)^2 - 1

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.