If g(x) = 2x2 + bx + 5 and g(1) = 4, what is the value of g(-1)? 1 2 3 7 10

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If g(x) = 2x2 + bx + 5 and g(1) = 4, what is the value of g(-1)? 1 2 3 7 10

Mathematics
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\(\large\color{black}{ \displaystyle g(x)=2x^2+bx+5 }\) correct?
yes sir

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Your given that \(\large\color{red}{ \color{black}{g(}1\color{black}{)=}\color{blue}{4} }\), so lets apply this. \(\large\color{black}{ \displaystyle g(x)=2x^2+bx+5 }\) for any function g(x)=function with x's. when you do g(1), every single x is replaced by a 1. This gets us: \(\large\color{black}{ \displaystyle g(\color{red}{1})=2(\color{red}{1})^2+b(\color{red}{1})+5 }\)
Now, we know that \(\large\color{red}{ \color{black}{g(}1\color{black}{)=}\color{blue}{4} }\) So, we can substitute 4 instead of g(1), the following way: \(\large\color{black}{ \displaystyle \color{blue}{4}=2(\color{red}{1})^2+b(\color{red}{1})+5 }\)
All you need to do know is to simplify and solve for b:)
i still need help sir solving for b @SolomonZelman
\(\large\color{black}{ \displaystyle \color{blue}{4}=2(\color{red}{1})^2+b(\color{red}{1})+5 }\) ok, what is `2(1)²` equal to?
2?
yes
So lets write that \(\large\color{black}{ \displaystyle \color{blue}{4}=2+b(\color{red}{1})+5 }\)
b(1) is b•1, and that is just b. Right?
yes
\(\large\color{black}{ \displaystyle \color{blue}{4}=2+b+5 }\)
can you solve this, or need a little more help?
i need a little more help please
\(\large\color{black}{ \displaystyle \color{blue}{4}=2+b+5 }\) \(\large\color{black}{ \displaystyle \color{blue}{4}=7+b }\)
agree?
but do we not consider the b to be a imaginary 1 ?
lol, it seems as though you are having a bad day right now...
4=7+b ust subtract 7 from both sides
lol no sir i just want to understand it fully
\(\large\color{black}{ \displaystyle 4=7+b }\) \(\large\color{black}{ \displaystyle 4\color{magenta}{-7}=7+b \color{magenta}{-7} }\) \(\large\color{black}{ \displaystyle 4\color{magenta}{-7}=\cancel{7}+b \cancel{\color{magenta}{-7}} }\)
b=?
3
not exactly, but close...
b can be negative too:)
but my answer choices are not negative
then they are wrong, because the answer is -3.
Oh, we are not done yet....
the answer choices are for g(-1)
and -3 that we found just now is the value of b
yes
Now we know our function entirely. g(x) = 2x² - 3x + 5
And now find g(-1), by plugging -1 instead of x.
g(x) = 2x² - 3x + 5 g(-1) = 2(-1)² - 3(-1) + 5=?
g(-1)=2 -3+5=4
???
or is it 10?
oh wait
i think it is 10 sir
g(-1) = 2(-1)² - 3(-1) + 5 g(-1) = 2 - - 3 + 5 g(-1) = 2 + 3 + 5 g(-1) = 10
correct
thank you so much you are awesome :)
You are welcome!

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