Solve y=2(x-5/6)^2-4

$$y = 2 ( x - \frac { 5 } { 6 } ) ^ { 2 } - 4$$

Solve for y

$$y=\frac{\left(6x-5\right)^{2}-72}{18}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-\frac{5}{6}\right)^{2}.

$$y=2\left(x^{2}-\frac{5}{3}x+\frac{25}{36}\right)-4$$

Use the distributive property to multiply 2 by x^{2}-\frac{5}{3}x+\frac{25}{36}.

$$y=2x^{2}-\frac{10}{3}x+\frac{25}{18}-4$$

Subtract 4 from \frac{25}{18} to get -\frac{47}{18}.

$$y=2x^{2}-\frac{10}{3}x-\frac{47}{18}$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{2y+8}}{2}+\frac{5}{6}$$

$$x=\frac{\sqrt{2y+8}}{2}+\frac{5}{6}$$

Solve for x

$$x=-\frac{\sqrt{2y+8}}{2}+\frac{5}{6}$$

$$x=\frac{\sqrt{2y+8}}{2}+\frac{5}{6}\text{, }y\geq -4$$