To graph the function \( f(x) = -16x^2 + 25x \), we recognize that this is a quadratic function in the form \( ax^2 + bx + c \), where \( a = -16 \), \( b = 25 \), and \( c = 0 \) (since there is no constant term).
-
X-intercepts: To find the x-intercepts, we set \( f(x) = 0 \):
\[ -16x^2 + 25x = 0 \]
Factoring out \( x \):
\[ x(-16x + 25) = 0 \]
This gives us two solutions:
\[ x = 0 \quad \text{and} \quad -16x + 25 = 0 \Rightarrow x = \frac{25}{16} \approx 1.5625 \]
So, the x-intercepts are \( (0, 0) \) and \( \left( \frac{25}{16}, 0 \right) \approx (1.563, 0) \).
-
Interpretation of x-intercepts:
- The first x-intercept at \( (0, 0) \) means that the soccer ball is at ground level at the time of the kick (0 seconds).
- The second x-intercept at \( (1.563, 0) \) means that the soccer ball will return to the ground approximately 1.563 seconds after it has been kicked.
In conclusion, the correct interpretation of the x-intercept \( (1.563, 0) \) is:
The soccer ball will return to the ground 1.563 seconds after it has been kicked.
Thus, the answer is:
- Response: \( (1.563, 0) \); The soccer ball will return to the ground 1.563 seconds after it has been kicked.
1 answer