What is the answer to this problem?

Difference = 5.6 which makes C the right answer.

Step-by-step explanation:

You have to determine g(x) before doing anything

g(x) = ax^2 + bx + c

g(0) =  c

c = 9 from the table

g(x) = ax^2 + b(x) + 9

g(1) = a + b + 9 = 33           multiply this equation by 2

g(1) = 2a + 2b + 18 = 66     Subtract 18 from both sides

2a + 2b = 66 - 18

2a + 2b = 48                       (1)

=====================

g(2) = 4a + 2b + 9  = 25     Subtract 9 from both sides

4x + 2b = 25 - 9

4x + 2b = 16                        (2)

===============    

Subtract (1) from (2)

4a + 2b = 16

2a + 2b = 48                        Subtract

2a = -       32                        Divide by 2

2a/2 =   -32/2

a = - 16

=================

Solve for b

2a + 2b = 48                         Let a = - 16

2(-16) + 2b = 48                    Simplify the left

-32 + 2b = 48                        Add 32

2b = 48 + 32                         Simplify the right

2b = 80                                 Divide by 2

b = 80/2                  

b = 40

=================

Complete equation

g(x) = -16x^2 + 40x + 9

The next step is to put the two equations into max/min state by completing the square.

Completing the square for f(x)

I am going to present you with the completed square with some guiding steps. First f(x)

f(x) = - 16(x^2 - 42x/16 +    ) + 12

f(x) = - 16(x^2 - 42/16 + (42/32)^2 ) + 12 + 42^2/(32*2)

f(x) = -16(x - 42/32)^2 + 12 + 26.5625

f(x) = - 16( x - 42/32)^2 + 39.5625

Use the same procedure for g(x)

g(x) = -16x^2 + 40x + 9

g(x) = -16(x^2 + 40x/16 +  ) + 9

g(x) = -16(x^2 + 40x/16 + (40/(16*2) )^2  )

g(x) = -16(x - 40/32)^2 + 9 + 40^2 / 32*2

g(x) = -16(x - 40/32)^2 + 34

=======================

The max height for g(x) = 34

The max height for f(x) = 39.56

The difference = 5.56

Graph

Red: g(x)

blue: f(x)

Answer C

If you know calculus, the question is much much shorter.

answer: it is d

step-by-step explanation:

sas (side angle side)

aa (angle angle)

sss(side side side)

sas find two sides with an angle in between

aa is finding two angles and the third will add up to 180

sss find all sides

step-by-step explanation: