Solve y=-1(x-1)(x-4)

$$y = - 1 ( x - 1 ) ( x - 4 )$$

Solve for y

$$y=-\left(x-4\right)\left(x-1\right)$$

Solution Steps

Use the distributive property to multiply -1 by x-1.

$$y=\left(-x+1\right)\left(x-4\right)$$

Use the distributive property to multiply -x+1 by x-4 and combine like terms.

$$y=-x^{2}+5x-4$$

Solve for x (complex solution)

$$x=\frac{\sqrt{9-4y}+5}{2}$$

$$x=\frac{-\sqrt{9-4y}+5}{2}$$

Solve for x

$$x=\frac{\sqrt{9-4y}+5}{2}$$

$$x=\frac{-\sqrt{9-4y}+5}{2}\text{, }y\leq \frac{9}{4}$$