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

yes because there is exactly one y value for every x value

for function there can't be more than one value for every x value

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.