how do you put y=.0048x^3-0.72x^2+36x-500 into y=a(x-h)^3+k form?

Question

please help me as soon as possible! I would really apprecitae it. :)

Answer 1

No answer, just a bit of discussion and speculation. . .

.

y = 0.0048x^3 - 0.72x^2 + 36x - 500

Let's get the 0.0048 out first.

y = 0.0048(x^3 - 15x^2 + 7500x - 312500/3)

Let's look at (x-h)^3

(x-h)^3 = x^3 -3hx^2 + 3h^2x + h^3

If the -15 in -15x^2 is like the -3h in -3hx^2, that would mean h = 5.

But that would make 3h^2x = 75x, which wouldn't match 7500x.

I think it would work if the original problem had 0.36x instead of 36x, but it doesn't so. . .

I think it would also work if the original problem had -7.2x^2 instead of -0.72x^2. . .

I'm not sure if y = 0.0048x^3 - 0.72x^2 + 36x - 500 can be put in y = a(x-h)^3 + k form.