Iwill give brainliest if you answer

a = 6/5, b = -48/5, and c = 72/5

See attached photo for graph

Step-by-step explanation:

We know that the solutions are x = 2, and x = 6.  These are the points where the graph crosses the x axis.  We can work backwards and get the equation as follows...

x = 2, this means that x - 2 = 0 is a factor

x = 6, this means that x - 6 = 0 is a factor

So we have

(x - 2)(x - 6)       now foil this to get a function...

f(x) = x² - 8x + 12       *But this isn't the function.  We write it like this...

f(x) = n(x² - 8x + 12)    because we don't know for sure that the 'n' value is.  There might be scalar multiple for the function.  We do know that f(1) = 6, so we have

f(1) = n[1² - 8(1) + 12]        now solve for n, substitute f(1) for 6

6 = n(5)

So n = 6/5,  now our function is

(6/5)(x² - 8x + 12)          distribute and simplify...

(6/5)x² - (6/5)8x + (6/5)12

      (6/5)x² - (48/5)x + 72/5

So a = 6/5, b = -48/5, and c = 72/5