Solve y=3*(x-9/2)^2-3/4

$$y = 3 \cdot ( x - \frac { 9 } { 2 } ) ^ { 2 } - \frac { 3 } { 4 }$$

Solve for y

$$y=3\left(x-5\right)\left(x-4\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-\frac{9}{2}\right)^{2}.

$$y=3\left(x^{2}-9x+\frac{81}{4}\right)-\frac{3}{4}$$

Use the distributive property to multiply 3 by x^{2}-9x+\frac{81}{4}.

$$y=3x^{2}-27x+\frac{243}{4}-\frac{3}{4}$$

Subtract \frac{3}{4} from \frac{243}{4} to get 60.

$$y=3x^{2}-27x+60$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{12y+9}}{6}+\frac{9}{2}$$

$$x=\frac{\sqrt{12y+9}}{6}+\frac{9}{2}$$

Solve for x

$$x=-\frac{\sqrt{12y+9}}{6}+\frac{9}{2}$$

$$x=\frac{\sqrt{12y+9}}{6}+\frac{9}{2}\text{, }y\geq -\frac{3}{4}$$