Category Archives: Regents

Get the Math and the Points Aug 18 CC Algebra I Regents #30

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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 🙂

 

Get the Math and the Points Aug 2018 CC Alg I Regents #28

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qf
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?