SOLUTION: y=x^2-4 - having trouble

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Question 744667: y=x^2-4 - having trouble
Found 3 solutions by MathLover1, erika514, Alan3354:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

general form of quadratic equation is y=ax%5E2%2Bbx%2Bc
you are given: y=x%5E2-4; means a=1, b=0, and c=-4
use quadratic formula to find solutions:

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2-4=0 (note: since the polynomial does not have an "x" term, the 2nd coefficient is zero. In other words, b=0. So that means the polynomial really looks like x%5E2%2B0%2Ax-4=0 notice a=1, b=0, and c=-4)





x+=+%280+%2B-+sqrt%28+%280%29%5E2-4%2A1%2A-4+%29%29%2F%282%2A1%29 Plug in a=1, b=0, and c=-4




x+=+%280+%2B-+sqrt%28+0-4%2A1%2A-4+%29%29%2F%282%2A1%29 Square 0 to get 0




x+=+%280+%2B-+sqrt%28+0%2B16+%29%29%2F%282%2A1%29 Multiply -4%2A-4%2A1 to get 16




x+=+%280+%2B-+sqrt%28+16+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%280+%2B-+4%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%280+%2B-+4%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%280+%2B+4%29%2F2 or x+=+%280+-+4%29%2F2


Lets look at the first part:


x=%280+%2B+4%29%2F2


x=4%2F2 Add the terms in the numerator

x=2 Divide


So one answer is

x=2




Now lets look at the second part:


x=%280+-+4%29%2F2


x=-4%2F2 Subtract the terms in the numerator

x=-2 Divide


So another answer is

x=-2


So our solutions are:

x=2 or x=-2




graph:
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-4%29+

Answer by erika514(39) About Me  (Show Source):
You can put this solution on YOUR website!
Hi there....don't worry we'll get through it! Here we go.

What we need to do is factor x^2-4. This equation is what we call a perfect square binomial which means we will have two binomials(expressions with terms of 2 different degrees, example:4 has a degree of 0, x^2 has a degree of 2) that are opposites (one number is positive and one number is negative but the have the same constant) of each other that equal x minus the square root of our constant term. So when factor, we should get (x-2)(x+2) because the square root of 4 is 2. Also -2 and 2 are opposites(one is positive, one is negative). We can check our factoring to make sure it is correct by using the FOIL(first, inner, outer,last) method. So what we are going to do is multiply the first two terms, x and x, together. When we multiply we get x^2. next we multiply the outer terms x and -2 together to get-2x, then we multiply our inner terms, 2 and x to get 2x and our last terms, -2 and 2, to get -4. We can add -2x and 2x, and they cancel, so we are left with x^2-4, which is our original binomial. That means that our final answer for y is y=(x-2)(x+2). Good luck, hope this helps(sorry it was so long!)and let me know of any other questions. :)

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
y=x^2-4 - having trouble
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x^2 - 4 = 0
x^2 = 4
x = -2, x = 2