Solve y=1/2(x-5)^2-8

$$y = \frac { 1 } { 2 } ( x - 5 ) ^ { 2 } - 8$$

Solve for y

$$y=\frac{\left(x-9\right)\left(x-1\right)}{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-5\right)^{2}.

$$y=\frac{1}{2}\left(x^{2}-10x+25\right)-8$$

Use the distributive property to multiply \frac{1}{2} by x^{2}-10x+25.

$$y=\frac{1}{2}x^{2}-5x+\frac{25}{2}-8$$

Subtract 8 from \frac{25}{2} to get \frac{9}{2}.

$$y=\frac{1}{2}x^{2}-5x+\frac{9}{2}$$

Solve for x (complex solution)

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

$$x=\sqrt{2\left(y+8\right)}+5$$

Solve for x

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

$$x=\sqrt{2\left(y+8\right)}+5\text{, }y\geq -8$$