What is f(x)=x^2-1.5f(x)+3 ?

The solution to f(x)=x^2-1.5f(x)+3 is Parabola with (h,k)=(0,1.2),p=0.625

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f(x)=x^2-1.5f(x)+3

f (x) = x^{2} - 1.5 f (x) + 3

(h, k) = (0, 1.2), p = 0.625

Solution steps

y = x^{2} - 1.5 y + 3

Rewrite

y = x^{2} - 1.5 y + 3

in the standard form:

4 \cdot 0.625 (y - 1.2) = (x - 0)^{2}

Therefore parabola properties are:

(h, k) = (0, 1.2), p = 0.625

y - 2 y - 3 y = 4 x^{2} + x - 5

(y + 2)^{2} = - 16 (x - 1)

x^{2} + 14 x - 2 y + 53 = 0

y = - x^{2} + 12 x - 35

(y - 7)^{2} = (x - 1)

What is f(x)=x^2-1.5f(x)+3 ?
The solution to f(x)=x^2-1.5f(x)+3 is Parabola with (h,k)=(0,1.2),p=0.625