Solve y=1/20(x-2)^2-1

$$y = \frac { 1 } { 20 } ( x - 2 ) ^ { 2 } - 1$$

Solve for y

$$y=\frac{\left(x-2\right)^{2}-20}{20}$$

Solution Steps

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

$$y=\frac{1}{20}\left(x^{2}-4x+4\right)-1$$

Use the distributive property to multiply \frac{1}{20} by x^{2}-4x+4.

$$y=\frac{1}{20}x^{2}-\frac{1}{5}x+\frac{1}{5}-1$$

Subtract 1 from \frac{1}{5} to get -\frac{4}{5}.

$$y=\frac{1}{20}x^{2}-\frac{1}{5}x-\frac{4}{5}$$

Solve for x (complex solution)

$$x=-2\sqrt{5y+5}+2$$

$$x=2\sqrt{5y+5}+2$$

Solve for x

$$x=-2\sqrt{5y+5}+2$$

$$x=2\sqrt{5y+5}+2\text{, }y\geq -1$$