Answer:
A and D
Explanation:
A is correct as x must be any real number to yield a proper f(x) value.
B is incorrect, as a value of x=0 would mean f(x) = 0 which is outside the listed range.
C is incorrect as the equation is a quadratic (highest exponent is ^2) which forms a parabola shape on a graph and therefore does not infinitely decrease.
D is correct. To find a maximum or turning point, we can take the derivative of the function and set it to 0, as the slope at any turning point will always be 0:
f'(x) = -8x
0 = -8x
x = 0
So, the maximum occurs where x=0
f(x) = -4x^2
f(x) = -4(0)^2
f(x) = 0
This means the y-value is also 0, meaning that (0,0) is our maximum.
E is incorrect. Since the maximum is only just on the x-axis (0,0) it only touches the x-axis once so it only has one x-intercept.
Hope this helped!