Solve y=3{left(x-7/3right)}^2-16/3

$$y=3 { \left(x- \frac{ 7 }{ 3 } \right) }^{ 2 } - \frac{ 16 }{ 3 }$$

Solve for y

$$y=\left(x-1\right)\left(3x-11\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-\frac{7}{3}\right)^{2}.

$$y=3\left(x^{2}-\frac{14}{3}x+\frac{49}{9}\right)-\frac{16}{3}$$

Use the distributive property to multiply 3 by x^{2}-\frac{14}{3}x+\frac{49}{9}.

$$y=3x^{2}-14x+\frac{49}{3}-\frac{16}{3}$$

Subtract \frac{16}{3} from \frac{49}{3} to get 11.

$$y=3x^{2}-14x+11$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{3y+16}+7}{3}$$

$$x=\frac{\sqrt{3y+16}+7}{3}$$

Solve for x

$$x=\frac{-\sqrt{3y+16}+7}{3}$$

$$x=\frac{\sqrt{3y+16}+7}{3}\text{, }y\geq -\frac{16}{3}$$