contestada

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 of x having x intercepts at ordered pairs 0, 0 and 0, 20. The vertex is at 10, 15.

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? (6 points)

Part B: What is an approximate average rate of change of the graph from x = 12 to x = 15, and what does this rate represent? (4 points)

The graph below shows the height of a kicked soccer ball fx in feet depending on the distance from the kicker x in feet Graph of quadratic function f of x havin class=

Respuesta :

Because the vertex of the parabola is at (10,15), its equation is of the form
y = a(x-10)² + 15

The graph goes through (0,0), therefore
a(0 - 10)² + 15 = 0
100a = -15
a = -0.15

The equation is 
y = f(x) = -0.15(x - 10)² + 15

The graph is shown below.

Part A
Note that y = f(x).

The x-intercepts identify values where the function or  y=0. The x-intercepts occur at x=0 and x=20, or at (0,0) and (20,0).

The maximum value of y occurs at the vertex (10, 15) because the curve is down due to the negative leading coefficient of -0.15.

The curve increases in the interval x = (-∞, 10) and it decreases in the interval x = (10, ∞).

Part B
When x=12, y = -0.15(12 - 10)² + 15 = 14.4
When x=15, y = -0.15(15 - 10)² + 15 = 11.25

The average rate of change between x =12 to x = 15 is
(11.25 - 14.4)/(15 - 12) = -1.05

This rate of change represents the slope of the secant line from A to B. It approximates the rate at which f(x) decreases in the interval x =[12, 15].

Ver imagen Аноним
facundo3141592

By analyzing the graph we will see that:

A)

  • The x-intercepts are the distances at which the ball is on the ground.
  • The maximum represents the distance at which the height of the ball is maximum.
  • The increasing interval is from x = 0 to x = 10
  • The decreasing interval is from x = 10 to  x = 20.

B) the average rate of change in that interval is -4/3.

How to interpret the graph of a quadratic function?

Here the quadratic graph represents the height of a ball as a function of the horizontal distance to the kicker.

A) The x-intercepts would represent the distances where the ball is on the ground (so the distance when the ball is kicked is x = 0, and the distance when the ball falls again to the ground is the other x-intercept).

The maximum value of the graph represents the maximum height that the ball reaches.

By looking at the graph, we can see that the ball height increases from:

x = 0 to x = 10

And the ball decreases from:

x = 10 to x = 20.

This means that as the ball distance increases, the height increases (on the first interval) or decreases (on the second interval).

B) For a function f(x), the average rate of change on an interval [a, b] is given by:

(f(b) - f(a))/(b - a).

Then here we want to find the rate of change in the interval [12, 15], so we will get:

(f(15) - f(12))/(15 - 12) = ( 10 - 14)/3 = -4/3.

This rate means that in the given interval, the height of the ball decreases.

If you want to learn more about quadratic equations, you can read:

https://brainly.com/question/1214333

Otras preguntas