Solve y=-(x+3/2)^2+1/4

$$y = - ( x + \frac { 3 } { 2 } ) ^ { 2 } + \frac { 1 } { 4 }$$

Solve for y

$$y=-\left(x+1\right)\left(x+2\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+\frac{3}{2}\right)^{2}.

$$y=-\left(x^{2}+3x+\frac{9}{4}\right)+\frac{1}{4}$$

To find the opposite of x^{2}+3x+\frac{9}{4}, find the opposite of each term.

$$y=-x^{2}-3x-\frac{9}{4}+\frac{1}{4}$$

Add -\frac{9}{4} and \frac{1}{4} to get -2.

$$y=-x^{2}-3x-2$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{1-4y}-3}{2}$$

$$x=\frac{\sqrt{1-4y}-3}{2}$$

Solve for x

$$x=\frac{-\sqrt{1-4y}-3}{2}$$

$$x=\frac{\sqrt{1-4y}-3}{2}\text{, }y\leq \frac{1}{4}$$