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

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

Solve for y

$$y=-\frac{\left(x-3\right)\left(x+5\right)}{8}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

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

Use the distributive property to multiply -\frac{1}{8} by x^{2}+2x+1.

$$y=-\frac{1}{8}x^{2}-\frac{1}{4}x-\frac{1}{8}+2$$

Add -\frac{1}{8} and 2 to get \frac{15}{8}.

$$y=-\frac{1}{8}x^{2}-\frac{1}{4}x+\frac{15}{8}$$

Solve for x (complex solution)

$$x=-2\sqrt{4-2y}-1$$

$$x=2\sqrt{4-2y}-1$$

Solve for x

$$x=-2\sqrt{4-2y}-1$$

$$x=2\sqrt{4-2y}-1\text{, }y\leq 2$$