Question

Find the vertex of the graph of the function.

f(x) = 2x2 - 8x + 6

Answer 1

( 2, -2)

( 3, -1)

( -1, 3)

( -2, 2)

Answer 2

i got ( 3, -1) am i right

Answer 3

-StudyShark- plez help

Answer 4

Hey c:

Answer 5

\[\Large\rm f(x)=2x^2-8x+6\]Need a 1 coefficient on the square term.
So factoring out a 2 from each of the x terms gives us:\[\Large\rm f(x)=2(\color{orangered}{x^2-4x})+6\]We need to complete the square on this orange part:\[\Large\rm \left(\frac{b}{2}\right)^2=\left(\frac{-4}{2}\right)^2=(-2)^2=4\]This is the value that completes the square for us.
So we'll add 4 to complete our square. But we'll also subtract 4 to keep things balanced.\[\Large\rm f(x)=2(\color{orangered}{x^2-4x+4}-4)+6\]Bringing the -4 out of the brackets, apply the 2 to it,\[\Large\rm f(x)=2(\color{orangered}{x^2-4x+4})-8+6\]Then our perfect square will simplify down to: \(\Large\rm \left(x+\frac{b}{2}\right)^2\)

Answer 6

\[\Large\rm f(x)=2(x-2)^2-8+6\]

Answer 7

So it looks like we end up with:\[\Large\rm f(x)=2(x-2)^2-2\]

Answer 8

Any of those steps look too confusing? :o

Answer 9

ohh so ir would be (2,-2)

Answer 10

it*

Answer 11

Yes.

Answer 12

can i as another question

Answer 13

sure.

Answer 14

State how many imaginary and real zeros the function has.

f(x) = x4 - 8x3 + 17x2 - 8x +16
0 imaginary; 4 real

2 imaginary; 2 real

3 imaginary; 1 real

4 imaginary; 0 real
i think the answer is 0 imaginary; 4 real

Answer 15

but i wanted to be sure

Answer 16

Ummm this involves using De'Cartes Rule of Signs I think.
You plug in -x for your x's and count the sign changes I think?
Mmm I better go look it up a sec.

Answer 17

Hmm I'm not sure how they want you to figure this problem out....
De'Cartes Rule of Signs tells us how many real roots we `potentially` could have.

Counting the sign changes:
We can have `four`, `two`, or `zero` positive real roots.
You'll have no negative roots when you apply the second part of the theorem.

But then to determine further... I guess you have to apply the Rational Root Theorem maybe?

Check all the factors of 16 to see which one will be a root of the polynomial, and then go through the long process of long division.

Maybe there is a better way, ugh...

But it turns out that it's `2 real`, `2 complex`.
How did you come to the conclusion of `4 real`, `0 complex`?

Answer 18

thanks...i think my answer is right i just wanted to make sure

Answer 19

thank you for all your help

Answer 20

But it's not right :o
Did you read what I said?