To solve a quadratic equation ax^2 + bx + c = 0, wecan use the quadratic formula above given on the Regents Reference Sheet.

In order to find out if a solution is rational or irrational, we focus on the algebra under the radical: b^2 – 4ac: If b^2 – 4ac is a perfect square, then when we take the square root, we will get a rational number but if b^2 – 4ac is not a perfect square (like 4, 9, 16 etc), then the solution will be irrational.

In the equation 2x^2 + 3x – 10 =0, a=2, b=3 and c = -10
Once you substitute in those numbers into b^2 – 4ac, do you get a perfect square or not?

For this question, use the TI-84 to find the x values that make y=0.  Use the table and then check your answers on the graph.  Show and explain all your work.

I. Doubling is definitely exponential
II.  1 inch every 4 days is a linear function
III. 5% every 3 years is a percent change and is therefore exponential

Since this question does not ask us to solve, we can look at the structure of the equations.
We need to first notice that the second equation in all the answer choices is identical to the one given.
Therefore, all of our energy should be directed at the top(first) equation so we will  compare the top equations in all 4 answers.
The correct answer will be a multiple of the top given equation:

Answer (1):   -2x – 2y = -6 almost looks like -2(x – y =3)
Answer (2):  -2x + 2y = 3 (if you multiply -2(x – y =3), the right hand side will have to be -6
Answer (3):  2x – 2y = 6 (this looks a LOT like x – y = 3!!!)
Answer (4): 3x + 3y = 9 almost looks like 3(x – y = 3) but not quite