Question

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


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10

Answer 1

@SolomonZelman

Answer 2

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

Answer 3

yes sir

Answer 4

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:

\(\large\color{black}{ \displaystyle g(\color{red}{1})=2(\color{red}{1})^2+b(\color{red}{1})+5 }\)

Answer 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:

\(\large\color{black}{ \displaystyle \color{blue}{4}=2(\color{red}{1})^2+b(\color{red}{1})+5 }\)

Answer 6

All you need to do know is to simplify and solve for b:)

Answer 7

i still need help sir solving for b @SolomonZelman

Answer 8

\(\large\color{black}{ \displaystyle \color{blue}{4}=2(\color{red}{1})^2+b(\color{red}{1})+5 }\)

ok, what is `2(1)²` equal to?

Answer 9

2?

Answer 10

yes

Answer 11

So lets write that
\(\large\color{black}{ \displaystyle \color{blue}{4}=2+b(\color{red}{1})+5 }\)

Answer 12

b(1) is b•1, and that is just b.

Right?

Answer 13

yes

Answer 14

\(\large\color{black}{ \displaystyle \color{blue}{4}=2+b+5 }\)

Answer 15

can you solve this, or need a little more help?

Answer 16

i need a little more help please

Answer 17

\(\large\color{black}{ \displaystyle \color{blue}{4}=2+b+5 }\)
\(\large\color{black}{ \displaystyle \color{blue}{4}=7+b }\)

Answer 18

agree?

Answer 19

but do we not consider the b to be a imaginary 1 ?

Answer 20

lol, it seems as though you are having a bad day right now...

Answer 21

4=7+b

ust subtract 7 from both sides

Answer 22

lol no sir i just want to understand it fully

Answer 23

\(\large\color{black}{ \displaystyle 4=7+b }\)
\(\large\color{black}{ \displaystyle 4\color{magenta}{-7}=7+b \color{magenta}{-7} }\)
\(\large\color{black}{ \displaystyle 4\color{magenta}{-7}=\cancel{7}+b \cancel{\color{magenta}{-7}} }\)

Answer 24

b=?

Answer 25

3

Answer 26

not exactly, but close...

Answer 27

b can be negative too:)

Answer 28

but my answer choices are not negative

Answer 29

then they are wrong, because the answer is -3.

Answer 30

Oh, we are not done yet....

Answer 31

the answer choices are for g(-1)

Answer 32

and -3 that we found just now is the value of b

Answer 33

yes

Answer 34

Now we know our function entirely.
g(x) = 2x² - 3x + 5

Answer 35

And now find g(-1), by plugging -1 instead of x.

Answer 36

g(x) = 2x² - 3x + 5

g(-1) = 2(-1)² - 3(-1) + 5=?

Answer 37

g(-1)=2 -3+5=4

Answer 38

???

Answer 39

or is it 10?

Answer 40

oh wait

Answer 41

i think it is 10 sir

Answer 42

g(-1) = 2(-1)² - 3(-1) + 5
g(-1) = 2 - - 3 + 5
g(-1) = 2 + 3 + 5
g(-1) = 10

Answer 43

correct

Answer 44

thank you so much you are awesome :)

Answer 45

You are welcome!