What is f(x)=4x^2-x+3.2f(x) ?

The solution to f(x)=4x^2-x+3.2f(x) is Parabola with (h,k)=(0.125,0.02840…),p=-0.1375

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f(x)=4x^2-x+3.2f(x)

f (x) = 4 x^{2} - x + 3.2 f (x)

(h, k) = (0.125, 0.02840 \dots), p = - 0.1375

Solution steps

y = 4 x^{2} - x + 3.2 y

Rewrite

y = 4 x^{2} - x + 3.2 y

in the standard form

4 (- 0.1375) (y - 0.02840 \dots) = (x - 0.125)^{2}

Therefore parabola properties are:

(h, k) = (0.125, 0.02840 \dots), p = - 0.1375

y = - x^{2} - 12 x - 36

y^{2} = 5 x - 14

x = \frac{1}{3} y^{2}

2 x^{2} - 2 x + k (x) - 3 = 0

(y + 3)^{2} = 16 (x - 9)

What is f(x)=4x^2-x+3.2f(x) ?
The solution to f(x)=4x^2-x+3.2f(x) is Parabola with (h,k)=(0.125,0.02840…),p=-0.1375