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
