Question

What is the vertex for the graph of y = 3x2 − 12x + 9?

a. (−2, 21)
b. (−2, 45)
c. (2, −3)
d. (2, −9)

Answer 1

The vertex is found by using: \(\ \sf \color{blue}{x } = \dfrac{-b}{2a} \) where A = 3 and B = -12

Therefore \(\ \sf \color{blue}{x} = \dfrac{-(-12)}{2(3)} \implies \dfrac{12}{6} \implies 2 \)

Thus, \(\ \sf \color{blue}{x} = 2 \)

Now substitute that into the function y = 3x^2 − 12x + 9.

You should always remember that y = f(x) and f(x) = y

It's because it's a function of "x". Whatever "x" is, it affects "y".

\(\ X \) is independent.
\(\ Y \) is dependent.

That being said, \(\ \sf f(\color{blue}{x}) = 3x^2 − 12x + 9\)

Since x = 2, you sub that into f(x), so, \(\ \sf F(\color{blue}{2}) = 3(\color{blue}{2})^2 - 12(\color{blue}{2}) + 9 \)

What does this simplify to?

Once you have simplified this, that is your vertex. It'll be in a coordinate pair. I'll explain the other part when you simplify this :}

Answer 2

I think is d .. idk did you tried doing the graph?

Answer 3

thanks!

Answer 4

It's not "D" . . .

Answer 5

what is it then?

Answer 6

Look at my explanation above. It's a violation of the CoC to give out direct answers. You should know that people who give direct answers out are very likely they're guessing, most of the time it's always wrong. Like now.

Answer 7

Um i wasnr giving no direct answer i said what i thought it was no need to be rude.
clearly i said idk.. cant read ?

Answer 8

Can't spell?

Answer 9

not gonna ruin her question by arguing with an immature person like you , be gone! bye

Answer 10

ok no need to fight on my question

Answer 11

sorry i couldn't help Shadowgirl15 :/

Answer 12

I'm not fighting, I'm just stating the truth. It's on you if you want to take it.


You can refer to my explanation above to get your answer. I can't give it to you.

Answer 13

ok you are being rude @tHe_FiZiCx99 but thanks anywaay

Answer 14

How am I being rude...

Answer 15

@lindaa19 its ok thanks anyway

Answer 16

no problem @Shadowgirl15

Answer 17

just because she didn't spell everythng correctly doesn't mean she can't spell at all maybe she is just typing fast @tHe_FiZiCx99

Answer 18

She said I can't read, I just 'returned' her insult.

Answer 19

bucause you completely disregarded what she said im not saying one of you is right or wrong but I talked to @lindaa19 @tHe_FiZiCx99

Answer 20

@tHe_FiZiCx99 are you gonna get at me for not spelling right now?

Answer 21

I honestly tried to help you. I don't really care if you do or don't take my advice. It won't affect me at all in any possible way.

Toodles ~