Solve y=-1/12(x-4)^2+3

$$y = - \frac { 1 } { 12 } ( x - 4 ) ^ { 2 } + 3$$

Solve for y

$$y=-\frac{\left(x-10\right)\left(x+2\right)}{12}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.

$$y=-\frac{1}{12}\left(x^{2}-8x+16\right)+3$$

Use the distributive property to multiply -\frac{1}{12} by x^{2}-8x+16.

$$y=-\frac{1}{12}x^{2}+\frac{2}{3}x-\frac{4}{3}+3$$

Add -\frac{4}{3} and 3 to get \frac{5}{3}.

$$y=-\frac{1}{12}x^{2}+\frac{2}{3}x+\frac{5}{3}$$

Solve for x (complex solution)

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

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

Solve for x

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

$$x=2\sqrt{9-3y}+4\text{, }y\leq 3$$