Final answer:
The function f(x) = -(x+7)(x+9) has two x-intercepts at (-7,0) and (-9,0), and one y-intercept at (0, -63).
Step-by-step explanation:
To find the x-intercept and y-intercept for the function f(x) = -(x+7)(x+9), we need to determine the points where the graph of the function crosses the x-axis and y-axis, respectively.
The x-intercept occurs where the function is equal to zero (f(x) = 0). Setting our function equal to zero, we get:
0 = -(x+7)(x+9)
This product equals zero when either (x+7) or (x+9) is zero, which gives us x = -7 or x = -9. Hence, we have two x-intercepts: (-7,0) and (-9,0).
To find the y-intercept, we set x to 0 in our function, resulting in:
f(0) = -(0+7)(0+9)
Thus, the y-intercept is f(0) = -63, which gives us the point (0, -63).