Please help this is my last question and I've been waiting 40 minutes

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:

Graph of quadratic function f(x) having x intercepts at ordered pairs (0, 0) and (16, 0). The vertex is at (8, 10).

Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the distance and height?

Part B: What is an approximate average rate of change of the graph from x = 8 to x = 13, and what does this rate represent?

check the picture below.

now, notice, each square in the grid is 2 units, so, x = 8, y = 10 and x = 13, y = 5

[tex]\bf slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby \begin{array}{llll} average\ rate\\ of\ change \end{array}\\\\ -------------------------------\\\\ \qquad \begin{cases} x_1=8\\ x_2=13 \end{cases}\implies \cfrac{f(13)-f(8)}{13-8}\implies \cfrac{5-10}{13-8}\implies \cfrac{-5}{5}\implies -1[/tex]

-1 or -1/1, or -(vertical distance) / (horizontal distance)

the negative means is dropping, and 1/1 means, for every foot going down, it moves farther away from the kicker by 1 foot.

alexrevelution alexrevelution · Answer 2 · 2019-05-07T16:32:10+02:00

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