Solve y=-9left(x^2-1/6right)+9/4

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

Solve for y

$$y=\frac{15}{4}-9x^{2}$$

Solution Steps

Use the distributive property to multiply -9 by x^{2}-\frac{1}{6}.

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

Add \frac{3}{2} and \frac{9}{4} to get \frac{15}{4}.

$$y=-9x^{2}+\frac{15}{4}$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{15-4y}}{6}$$

$$x=\frac{\sqrt{15-4y}}{6}$$

Solve for x

$$x=\frac{\sqrt{15-4y}}{6}$$

$$x=-\frac{\sqrt{15-4y}}{6}\text{, }y\leq \frac{15}{4}$$