Select all the true statements about the graph of \( f(x)=-4 x^{2}-40 x \).
It crosses the \( y \)-axis at \( (0,-40) \).
It crosses the \( x \)-axis at \( (0,0) \) and \( (-10,0) \).
Its axis of symmetry has the equation \( x=0 \).
It has a maximum point at \( (-5,100) \).
It is a parabola that opens upward.

Step 1 ：To find the y-intercept, plug in x=0: \(f(0) = -4(0)^2 - 40(0) = 0\). So, the point (0, 0) is where the graph of the function crosses the y-axis.

Step 2 ：To find the x-intercepts, plug in f(x) = 0: \(0=-4 x^{2}-40 x\). Factor the equation: \(0=(-4x)(x+10)\). So, the function crosses the x-axis at (0,0) and (-10,0).

Step 3 ：The parabola's axis of symmetry has the equation \(x=\frac{-b}{2a}\), where a = -4 and b = -40, so \(x=\frac{-(-40)}{2(-4)}=-5\). Thus, the axis of symmetry has the equation \(x=-5\).

Step 4 ：To find the maximum point, find \(f(-5)=-4(-5)^2 - 40(-5)=(-4)(25)+200=-100+200=100\). So, the maximum point of the parabola is at \((-5, 100)\).

Step 5 ：The parabola opens upward if a is positive. In this case, a = -4, meaning the parabola opens downward.