The quadratic function H(x) = (-4x - 5)(-x + 5) expands to 4x^2 - 15x - 25. This represents a parabolic curve, illustrating the relationship between the variable x and the function's output.
The expression H(x) = (-4x - 5)(-x + 5) represents a quadratic function. To find the expanded form, you can use the distributive property:
H(x) = (-4x - 5)(-x + 5)
H(x) = -4x(-x) + (-4x)(5) - 5(-x) - 5(5)
H(x) = 4x^2 - 20x + 5x - 25
Combine like terms:
H(x) = 4x^2 - 15x - 25
So, the expanded form of H(x) is 4x^2 - 15x - 25. This equation represents the relationship between the variable, which here is 'x', and the function's output, showcasing that it has a quadratic nature.