From the January 2016 Common Core Algebra I Regents

Notice we are looking for the x value — similar to #1 on this very same Regents!!
https://mathconfidence.com/2016/05/02/get-the-math-and-get-the-points-notice-x/

Input both equations into Y=…absolute value is found either under Math, Number or in the catalog which can be found by doing 2nd zero
For answer choice (1), when x = -2 both Y1 and Y2 are the same :)
For answer choice (2), when x = 2, Y1 = 4 while Y2 = 2
For answer choice (3), when x = 3, Y1 = 4.5 while Y2 = 3
For answer choice (4), when x = -6, here’s another snapshot with the table arrowed up to more negative numbers:

when x = -6, Y1 = 0 while Y2 = 6.

From the January 2016 Common Core Algebra I Regents

http://www.regentsprep.org/regents/math/algtrig/ate12/completesqlesson.htm

We can use the method of completing the square — see the link above
So far we have x^2 – 8x so we take 1/2 of -8 and square that to complete
(x –  4) (x – 4 ) giving x^2 – 8x + 16

trying answer (1) gives x^2 – 8x + 16 = 9  if we subtract 9 from each side we get:
x^2 – 8x + 7 = 0  close but no cigar

trying answer (2) gives x^2 – 8x + 16 = 23  if we subtract 23 from each side we get:
x^2 – 8x – 7 = 0  matches exactly!!!

OR

we can expand each answer and set it equal to zero to see which one matches the original whether on paper or on the TI-84
On the TI-84, set Y1 = x^2 – 8x – 7 and then set each answer choice to 0 and put into Y2 one by one
Try answer (1) by setting Y2 = (x – 4)^2 – 9, does it match Y1?
Try answer (2) by setting Y2 = (x – 4)^2 – 23, does it match Y1?  :)

From the January 2016 Common Core Algebra I Regents:

This is really a rate of change or slope question: (change in y) / (change in x)

For answer choice (1), it took 73 years to go up 5 cents not a lot of increase per year
For answer choice (2), 14-6 = 8 cents over 14 years (1985-1971)
For answer choice (3), 24 – 14 = 10 cents over 21 years (2006 – 1985)
For answer choice (4), 35 – 24 = 11 cents over only 6 years (2012 – 2006)

(We can see that the price change has been increasing by more cents as time goes on)
So which time interval had the most change per year?  Please see below

1st step: distribute x(x-12) and then add 34
so you will now have y = x^2 – 12 x +34  or you could type in:
y = x(x-12) +34 without even distributing
Put either of those into Y1 and try answer (1) in Y2, like this…not a match!!  The tables are different as is the graph!

Now try answer (2) below  also not a match

Next, choice (3) nope not a match

Choice 4 below, the tables match and the graphs are exactly the same — therefore we can only see one parabola!  You just got 2 more points :)

From the January 2016 Common Core Algebra I Regents

This is a reading and noticing question with no TI-83/4 needed.
5 points are shown on this line but only 3 are easy to read: (4,15), (8,30) and (12,45)

Let’s check out each of the multiple choice options:
(1) When x = 10, is y = 35? (look carefully!)
(2) Look at the first point at a ‘crosshair’, (4,15)  divide $15 by 4, what do you get?
You can also use (30 divided by 8 or 45 divided by 12)
(3) When x = 2, is y = 5?  (look carefully!)
(4)  You can still drive if you did not buy gas (as long as there is gas in the tank!!)

For student classwork/homework, here is the Word file:
Jan 2016 CC Alg I 2 Get the Math and the Points