Solve y=2(x-8)^2-5

$$y = 2 ( x - 8 ) ^ { 2 } - 5$$

Solve for y

$$y=2\left(x-8\right)^{2}-5$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-8\right)^{2}.

$$y=2\left(x^{2}-16x+64\right)-5$$

Use the distributive property to multiply 2 by x^{2}-16x+64.

$$y=2x^{2}-32x+128-5$$

Subtract 5 from 128 to get 123.

$$y=2x^{2}-32x+123$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{2y+10}}{2}+8$$

$$x=\frac{\sqrt{2y+10}}{2}+8$$

Solve for x

$$x=-\frac{\sqrt{2y+10}}{2}+8$$

$$x=\frac{\sqrt{2y+10}}{2}+8\text{, }y\geq -5$$