50 POINTS PLS HELP

Use the function f(x) = x2 − 6x + 3 and the graph of g(x) to determine the difference between the maximum value of g(x) and the minimum value of f(x). a parabola that opens down and passes through 0 comma 3, 3 comma 12, and 5 comma 8

3
6
12
18

18

Step-by-step explanation: pluging in -b/2a for first equation you get 3 plunging 3 in you get 6 solving for second equation you get -x^2+6x+3 pluging in -b/2a you get 3 then plugoing into equation you get 12 12-(-6)=18

I take it g(x) is given by this description:

a parabola that opens down and passes through 0 comma 3, 3 comma 12, and 5 comma 8

If we could see  the figure we'd known if (3,12) was the max they're talking about.  We'll have to check.

Opens down is a CDN, concave down negative, so a negative coefficient on the squared term.  Through (0,3), (3,12), (5,8)

g(x) = ax² + bx + c

3 = g(0) = c

g(x) = ax² + bx + 3

12=g(3) = 9a + 3b + 3

9 = 9a+3b

3 = 3a + b

8=g(5) = 25a + 5b +3

5 = 25a + 5b

1 = 5a + b

Subtracting the two equations '3=' and '1=' we get

2 = -2a

a = -1

b = 1 - 5a = 6

g(x) = -x² + 6x + 3 = -(x²  - 6x) + 3 = -(x² - 6x + 9) + 3 + 9 = 12-(x-3)²

and we see the max at x=3, y=12.  It would have been easier to show the graph or say that.

f(x) = x² - 6x + 3 = (x - 3)² + 3 - 9 = (x-3)² - 6

So this mas a minimum (the squared term can't get any less than zero) at x=3, y=-6

Distance between them is 12 - -6 = 18

18

step-by-step explanation: