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Answer :
Final answer:
The standard form of the function f(x) = -5x(x + 3)(x - 2)^2 is -5x^3 +15x^2. The y-intercept of the function is at the ordered pair (0, 0).
Explanation:
To find the standard form of the function f(x) = -5x(x + 3)(x - 2)^2, we first need to expand the expression:
- Begin by expanding the term (x - 2)^2. This becomes x^2 - 4x + 4.
- Next, let's expand -5x(x + 3)(x^2 - 4x + 4) by distributing the terms. This gives us -5x^3 + 20x^2 - 20x - 5x^2 + 20x - 20.
- Finally, combine the like-terms to get: -5x^3 +15x^2 -60x +60.
So the standard form of the function is -5x^3 +15x^2. Next, to find the y-intercept, substitute x = 0 into the function. This gives f(0) = -5(0)^3 + 15(0)^2 = 0. So the y-intercept is the ordered pair (0, 0).
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