Write the quadratic function g(x)= x^2 + 6x -2 in vertex form and give the vertex

The vertex form of this equation is y = (x + 3)^2 - 11

Step-by-step explanation:

In order to find the vertex form of the equation, we have to do a process called completing the square. The step by step instructions are below for you.

y = x^2 + 6x - 2

Add/Subtract the constant to the y side of the equation.

y + 2 = x^2 + 6x

Take half of the 6 coefficient (3) and then square it (9). Add that number to both sides.

y + 11 = x^2 + 6x + 9

Now you can factor the right side as a perfect square.

y + 11 = (x + 3)^2

Lastly we add/subtract the constant back to the right side.

y = (x + 3)^2 - 11

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.