Question

Using the completing-the-square method, find the vertex of the function f(x) = 2x2 − 8x + 6 and indicate whether it is a minimum or a maximum and at what point.

Maximum at (2, –2)
Minimum at (2, –2)
Maximum at (2, 6)
Minimum at (2, 6)

Answer 1

im stuck between a and be, i know those points are correct, however i do not know how to determine max. & min.

Answer 2

Can you show the work that you have so far?

Answer 3

show your work to complete the square

Answer 4

its all on my scrap paper.

Answer 5

believe me, you wouldnt be able to understand it lol

Answer 6

i cant even read it...

Answer 7

Can you type (at least some of) it up here?

Answer 8

so just do it again here

Answer 9

i dont know what i did honestly my nephew helped with mostly all of it

Answer 10

Are you aware of the property below?

\(\color{#000000 }{ \displaystyle x^2+2ax+a^2=(x+a)^2 }\)

Answer 11

barely.

Answer 12

Please expand the expression below:
\(\color{#000000 }{ \displaystyle (x+a)\cdot (x+a) }\)

Answer 13

i got it! thank you very much! i came up with answer choice B. he came back with the paperwork and explained to me what i jotted down so quickly lol.

Answer 14

Yes, B is right!

Answer 15

Thank you so much!

Answer 16

Refer to the attached plot.

Answer 17

\(\color{#000000 }{ \displaystyle f(x)=2x^2-8x+6}\)
\(\color{#000000 }{ \displaystyle f(x)=2\left(x^2-4x\right)+6}\)
\(\color{#000000 }{ \displaystyle f(x)=2\left(x^2-4x+0\right)+6}\)
\(\color{#000000 }{ \displaystyle f(x)=2\left(x^2-4x\color{blue}{+4}\color{red}{-4}\right)+6}\)
\(\color{#000000 }{ \displaystyle f(x)=2\left(x^2-4x\color{blue}{+4}\right)+2\cdot(\color{red}{-4})+6}\)
\(\color{#000000 }{ \displaystyle f(x)=2\left(x^2-2\cdot(2) x+2^2\right)-8+6}\)
\(\color{#000000 }{ \displaystyle f(x)=2\left(x-2\right)^2-2}\)

\(\color{#000000 }{ \displaystyle (h,k)=(2,-2)}\) is the vertex.
(And since parabola opens up, the vertex is minimum)