Question

I'll fan 

Answer 1

Remark: the x-intercepts are clearly (0, 0) and (20, 0), not (0, 0), (0, 20).

having the 2 x intercepts and the vertex we can draw the graph, check picture 1 attached.

Moreover, we can also determine the quadratic function as follows.

The quadratic function with roots a and b, is given by the equation:

f(x)=c(x-a)(x-b).

[ since f(a)=0, f(b)=0, f(x) must have one factor (x-a) and one (x-b)]

The x coordinates of the x intercepts are the roots of the function so with the roots given:

f(x)=c(x-0)(x-20)=cx(x-20), the vertex is at (10, 15) so

15=f(10)=c*10*(10-20)=c*10*(-10)=-100c
c=-15/100=-3/20

the quadratic function (expressed in factorized form) is

f(x)=-3/20x(x-20)

part A: the x intercept 0 is the point where the ball was hit, the x intercept 20 is the point where the ball fell back to the ground, 20 feet away from the kicker.

the function is increasing in the interval x∈(0, 10) and decreasing in x∈(10, 20) 
this means that the height is increasing in the interval  (0, 10) and decreasing as x goes through the interval (10,20)
the distance from the kicker is increasing during the whole interval (0, 20)

Part B: at x=15, f(x)=f(15)=-3/20*15(15-20)=$\frac{-3}{20}*15*(-5)= \frac{-3}{4}*3*(-5)= \frac{45}{4}$

at x=12, f(x)=f(12)=-3/20*12(12-20)=$\frac{-3}{20}*12*(-8)= \frac{-3}{5}*3*(-8)= \frac{72}{5}$

the average rate of change is the ratio of the differences in y to the differences in x : $\frac{y_1_5-y_1_2}{x_1_5-x_1_2}= \frac{\frac{45}{4}-\frac{72}{5}}{15-12}= -1.05$

so the average rate of change is -1.05. The minus, tells us that the height is decreasing in the following way: for 1 feet in distance, we are loosing 1.05 feet in height.  

Answer 2

Part A:The graph below shows the height of a kicked soccer ball f(x), in feet, depending on the distance from the kicker x, in feet  

X Intercept=(0,0) it represents the time the ball was not kicked at all  

X intercept=(16,0)  

the feet away from the starting point is 16ft the location or distance the ball is away from the starting point once landed.  

Maximum: is 10  

intervals:it increased(0 to 8) decreased (8 to 16)  

when the ball was 8 ft away from the kicker horizontally, it was 10 feet in the air then it landed an additional 8 feet away from the kicker that was 16 feet away one it landed after going a maximum of 10 feet.  

Part B: m=(y2 - y1) / (x2 - x1)  

(x1, y1) (x2, y2)  

(8,10) (13, 7)  

m = (7-10)/(13-8) = -3/5