Resolver y=2(x-1)^2-3

$$y = 2 ( x - 1 ) ^ { 2 } - 3$$

Ebatzi: y

$$y=2\left(x-1\right)^{2}-3$$

Ebazpidea

\left(x-1\right)^{2} zabaltzeko, erabili Newton-en binomioa \left(a-b\right)^{2}=a^{2}-2ab+b^{2}.

$$y=2\left(x^{2}-2x+1\right)-3$$

Erabili banaketa-propietatea 2 eta x^{2}-2x+1 biderkatzeko.

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

-1 lortzeko, 2 balioari kendu 3.

$$y=2x^{2}-4x-1$$

Ebatzi: x (complex solution)

$$x=-\frac{\sqrt{2y+6}}{2}+1$$

$$x=\frac{\sqrt{2y+6}}{2}+1$$

Ebatzi: x

$$x=-\frac{\sqrt{2y+6}}{2}+1$$

$$x=\frac{\sqrt{2y+6}}{2}+1\text{, }y\geq -3$$