Finding coordinates of the points of given functions

[idoliki]

Hey guys,

I thought I could solve the homework/preparing for the exam but I'm stuck on this one, anybody has idea how to do this? Also, explain it or youtube tutorial on this (I tried searching but nothing similar comes up, only simple equations). I'm stuck in doing the quadratic equation on exercise 2. a).

2. Consider the two functions:

. . . . .\(\displaystyle f(x)\, =\, -2x^2\, +\, 4x\, -\, \dfrac{3}{2}\, \mbox{ and }\, g(x)\, =\, 2x\, -\, 1\)

(a) Find the coordinates of the point(s) where the graph of f (x) intersects the x-axes, as well as the coordinates of the local minimum of the graph of f (x).
(b) Sketch the graphs of f (x) and g(x) on the same diagram of the Cartesian plane.
(c) Find the coordinates of the points of intersection of the graphs of f (x) and g(x).

If somebody could solve the a,b,c I would be really thankful. I need this badly guys.

Thanks very much!

 

[Otis]

I'm stuck in doing the quadratic equation on exercise 2. a).

2. Consider the two functions:

. . . . .\(\displaystyle f(x)\, =\, -2x^2\, +\, 4x\, -\, \dfrac{3}{2}\, \mbox{ and }\, g(x)\, =\, 2x\, -\, 1\)

(a) Find the coordinates of the point(s) where the graph of f (x) intersects the x-axes, as well as the coordinates of the local minimum of the graph of f (x).
(b) Sketch the graphs of f (x) and g(x) on the same diagram of the Cartesian plane.
(c) Find the coordinates of the points of intersection of the graphs of f (x) and g(x).

Please show us how far you got (i.e., list your steps), applying the Quadratic Formula (or other method) to the equation in exercise 2a, so that we may see where you got stuck.

Thank you.

 

[idoliki]

I tried solving a) < link to objectionable page removed >
then c) < link to objectionable page removed >
and then b) < link to objectionable page removed >

Could you confirm if this is correct, and are there any better way to do this? Or something I can improve? Thanks!