Dear New York High Schoolers,
Best on your Regents exams this week.
Make sure you get to school early and eat a good breakfast!
Do not leave early: Spend all the allotted time (3 hours — unless your IEP is for more time)
Eat a good breakfast
Go over the entire exam after you finish and check your work
Robin the Math Lady
The left hand side of the equation is almost a perfect square:
In order for it to be a perfect square: x^2 + 4x + ____ = 2 + ____
To find the number that completes the square take 1/2 of 4 and square it
So 4 gets added to both sides
Then the right side becomes 6
Then we can write the left side like this: (x + 2) ^2
So (x + 2)^2 = 6
then take the sqrt of both sides but do not forget the +/- with the sqrt
Then subtract 2 from both sides:
You will have two answers a plus and a minus and you can check your work by using the quadratic formula 🙂
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