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You have to give good answers or ask good questions.....and hope that peole give you some points....LOL!!!

12x^2 - 5x  = 2    subtract 2 from both sides

12x^2 - 5x - 2        factor as

(4x + 1) ( 3x - 2)

Here : https://web2.0calc.com/questions/hellllppppp_3

y = (x - 2)^2 + 6

y = 3( - 2)^2  + ( - 4 )

We have the form

y = a(x - h)^2 + k

When "a"  is positive, the parabola opens upward

The vertex  = (h, k)  = (2, -4 )

The axis of symmery  is  x  = h

The y intercept is found just as I described

The vertex is always the minimum when a parabola opens upward

y = 3(x - 2)^2 - 4

Vertex  = (2, - 4)

Axis of symmetry :  x  = 2

This parabola opens upward....therefore...the vertex is a minimum

y intercept : let x  = 0   and we have

y = 3(0-2)^2 - 4   =  3(-2)^2 - 4  =  3(4) - 4  = 12 - 4  = 10

Here's the graph :   https://www.desmos.com/calculator/w1tqaeu5yv

Correct...good job, PN   !!!!!

The parentheses don't matter......

y = [ 2x + 1 ]  = 2x + 1

Not sure it has a name......

f(x) = y

y = 2x + 1

We have the form  y  = mx + b

The y intercept  = (0, b)

So here...the y intercept  = 1  means the point (0, 1)

The slope is the value in front of the "x"  = 2  =  2/1

This means that y changes by 2  when x changes by 1

So....a second point on the graph  is  ( 0 + 1, 1 + 2)  = (1, 3)

Plot  (0, 2)  and (1, 3)....draw a line through them....this is your graph

Yes....if we had   (4, 9)  and (4, 11).....the axis of symmetry would be

y =  [ 9 + 11 ] / 2  =  20 / 2   =  10

I think that anyone who is a member can give you points....I just gave you a few!!!!