Solve y=0.9(x-4)^2+2

$$y = 0.9 ( x - 4 ) ^ { 2 } + 2$$

Solve for y

$$y=\frac{9\left(x-4\right)^{2}}{10}+2$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.

$$y=0.9\left(x^{2}-8x+16\right)+2$$

Use the distributive property to multiply 0.9 by x^{2}-8x+16.

$$y=0.9x^{2}-7.2x+14.4+2$$

Add 14.4 and 2 to get 16.4.

$$y=0.9x^{2}-7.2x+16.4$$

Solve for x (complex solution)

$$x=-\sqrt{\frac{10y-20}{9}}+4$$

$$x=\sqrt{\frac{10y-20}{9}}+4$$

Solve for x

$$x=-\frac{\sqrt{\frac{40y-80}{9}}}{2}+4$$

$$x=\frac{\sqrt{\frac{40y-80}{9}}}{2}+4\text{, }y\geq 2$$