The graph of f(x) = -x2 - 2x + 8 is shown. Which of the following describes all solutions for f(x)? O(x -x2 - 2x + 8) for all real numbers
O(-4,0), (-1,9), (0, 8), (2.0)
O(-4.0), (2,0)
O(x, y) for all real numbers

y-intercept is when x = 0:

So the y-intercept is (0, 8)

x-intercepts are when f(x) = 0:

Therefore:

So the x-intercepts are (-4, 0) and (2, 0)

The vertex is the turning point of the parabola.  The x-value of the vertex is the x-value between the 2 zeros (x-intercepts).

Therefore, the x-value of the vertex is

Substituting x = -1 into the function:

So the vertex is (-1, 9)

The domain is the input values, so x = all real numbers.

The range is the output values, so the range is

Therefore, (-4, 0), (-1, 9), (0, 8) and (2, 0) are solutions of the function, HOWEVER they are not ALL the solutions.

All solutions of the function are:

for all real numbers of x

The answer is in the image 

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

The answer is in the image 

The answer is in the image 

The answer is in the image 

The solution is given in the image below

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

Distance travelled in 15 min=15*900=13,500m

=13500/1000 km=13.5Km

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.