The x-intercept of a function represents the point at which the function crosses or touches the x-axis. In other words, it is the value of x at which the y-coordinate (f(x)) is equal to 0.
To find the x-intercepts of the function f(x) = -16x² + 25x, we set f(x) equal to 0 and solve for x:
-16x² + 25x = 0
Factor out x:
x(-16x + 25) = 0
Setting each factor equal to zero:
x = 0 or -16x + 25 = 0
Solving for x in the second equation:
-16x + 25 = 0
-16x = -25
x = -25/-16
x = 1.563
So the x-intercept is (1.563, 0).
Interpretation:
The x-coordinate of the x-intercept (1.563) represents the time (in seconds) at which the soccer ball returns to the ground after being kicked. Therefore, the interpretation is as follows:
(1.563, 0): The soccer ball will return to the ground 1.563 seconds after it has been kicked.
Therefore, the correct answer is:
(1.563, 0); The soccer ball will return to the ground 1.563 seconds after it has been kicked.
A soccer ball is kicked from the ground at an upward velocity of 25 feet per second. This situation can be represented by the function f(x)= -16x² + 25x. Graph the function. Identify the x-intercept(s) and interpret its meaning.
• (1.563, 0); The soccer ball will return to the ground 1.563 seconds after it has been kicked.
• (0.781, 9.766); The soccer ball will reach a maximum height of 9.766 feet 0.781 seconds after being kicked.
• (0, 1.563); The soccer ball will return to the ground 1.563 seconds after it has been kicked.
• (1.25, 0); The soccer ball will return to the ground 1.25 seconds after it has been kicked.
1 answer