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)

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)

mehek14 · Answer

since the first term is positive = $2x^2$
that means it is opening upwards so the vertex would be the minimum
that eliminates A and C

mehek14 · Answer

to find the vertex, use
$\dfrac{-b}{2a}$
in your equation, you have 
b = -8
a = 2
$\dfrac{-(-8)}{2*2}=\dfrac{8}{4}=2$
so x = 2

mehek14 · Answer

plug x = 2 into the equation

mehek14 · Answer

@boots_2000 can you do that?

anonymous · Answer

Yeah so is it maximum 2,6?

anonymous · Answer

@Mehek14

irishboy123 · Answer

it says "Using the completing-the-square method"

mehek14 · Answer

no did you plug in x = 2 in the equation

anonymous · Answer

yeah

welshfella · Answer

using completing the square:-

= 2(x^2 - 4x + 3)

= 2[(x - 2)^2  - c + 3]

can you tell me the value of c - can you remember from the last post?

mehek14 · Answer

$f(2)=2*2^2-8*2+6\2^2=4\2*4=8\8*2=16\8-16=-8$
add $-8+6$

irishboy123 · Answer

+1 @welshfella

anonymous · Answer

so its minimum? lol

mehek14 · Answer

$\color{#0cbb34}{\text{Originally Posted by}}$ @Mehek14
since the first term is positive = $2x^2$
that means it is opening upwards so the vertex would be the minimum
that eliminates A and C
$\color{#0cbb34}{\text{End of Quote}}$

welshfella · Answer

its a minimum but what are the coordinates at the minimum?

anonymous · Answer

2,6

mehek14 · Answer

$\color{#0cbb34}{\text{Originally Posted by}}$ @Mehek14
$f(2)=2*2^2-8*2+6\2^2=4\2*4=8\8*2=16\8-16=-8$
add $-8+6$
$\color{#0cbb34}{\text{End of Quote}}$

welshfella · Answer

No mehek has worked the y coordinate for you
you can also get from the completing the square method

anonymous · Answer

so 2,-2

mehek14 · Answer

yes

anonymous · Answer

could you guys come and help me quick when you're all done here?

welshfella · Answer

I'll carry from where i left off
2[(x - 2)^2  - c + 3]

c  = 4   because   -2^2 = + 4

= 2(x - 2)^2 - 1)
= 2(x - 2)^2 - 2

so the vertex is at ( 2,-2)

you get this by comparing your expression with the genarl form for the vertex

anonymous · Answer

please

welshfella · Answer

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