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Simplify: Let G(u)=4-3u-u^2. Find G(-2u)
- Thread starter lowraws
- Start date
Well, if you're ever uncertain of an answer, you can always check it yourself. In this case, the best way to check an answer is to pick a random value for u and see if the equation holds. Let's say u = 5. The original function then tells us:
\(\displaystyle G(u)=G(5)=4-3(5)-(5)^2=-36\)
If u = 5, then we know that -2u = -10. Let's plug that in:
\(\displaystyle G(-2u)=G(-10)=4-3(-10)-(-10)^2=-66\)
Your proposed solution is as follows:
\(\displaystyle G(-2u)=4+(6u^2+2u^3)\)
When u = 5, that should give us -66, if your solution is correct. Let's see if it does:
\(\displaystyle G(-2u)=4+[6(5)^2+2(5)^3]=404\)
Oops! So, it looks like your solution isn't correct. Now, let's go back to the drawing board to see if you can figure out why it's wrong. Start again with the original function, and we'll not assume any specific value for u.
\(\displaystyle G(u)=4-3u-u^2\)
Now, if you'd been asked to find G(3), how would you do that? How would you find G(7)? How would you find G(100)? How would you find G(q)? What does all of this suggest about how you might find G(-2u)?
\(\displaystyle G(u)=G(5)=4-3(5)-(5)^2=-36\)
If u = 5, then we know that -2u = -10. Let's plug that in:
\(\displaystyle G(-2u)=G(-10)=4-3(-10)-(-10)^2=-66\)
Your proposed solution is as follows:
\(\displaystyle G(-2u)=4+(6u^2+2u^3)\)
When u = 5, that should give us -66, if your solution is correct. Let's see if it does:
\(\displaystyle G(-2u)=4+[6(5)^2+2(5)^3]=404\)
Oops! So, it looks like your solution isn't correct. Now, let's go back to the drawing board to see if you can figure out why it's wrong. Start again with the original function, and we'll not assume any specific value for u.
\(\displaystyle G(u)=4-3u-u^2\)
Now, if you'd been asked to find G(3), how would you do that? How would you find G(7)? How would you find G(100)? How would you find G(q)? What does all of this suggest about how you might find G(-2u)?
Thanks for that informative reply.
Seems that I was multiplying u by -2u rather than substituting -2u for u.
My new answer is 4+6u-4u^2
Quadratic
-4u^2+6u+4 = 4u^2-6u-4 = 4u(u-2) 2(u-2)
Factors
(4u+2)(u-2)
u=-1/2 or u=2
Substituting 2 in my equation gives 4+(6*2)-4(4)=0
Substituting -1/2 in my equation gives 4+(6*-1/2) -4(1/4) =0
Both values work
Right or Wrong ?
Seems that I was multiplying u by -2u rather than substituting -2u for u.
My new answer is 4+6u-4u^2
Quadratic
-4u^2+6u+4 = 4u^2-6u-4 = 4u(u-2) 2(u-2)
Factors
(4u+2)(u-2)
u=-1/2 or u=2
Substituting 2 in my equation gives 4+(6*2)-4(4)=0
Substituting -1/2 in my equation gives 4+(6*-1/2) -4(1/4) =0
Both values work
Right or Wrong ?