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

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

Solve for y

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

Solution Steps

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

$$y=-\frac{3}{4}\left(x^{2}+6x+9\right)+1$$

Use the distributive property to multiply -\frac{3}{4} by x^{2}+6x+9.

$$y=-\frac{3}{4}x^{2}-\frac{9}{2}x-\frac{27}{4}+1$$

Add -\frac{27}{4} and 1 to get -\frac{23}{4}.

$$y=-\frac{3}{4}x^{2}-\frac{9}{2}x-\frac{23}{4}$$

Solve for x (complex solution)

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

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

Solve for x

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

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