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

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

Solve for y

$$y=-\frac{\left(1-x\right)\left(x-5\right)}{4}$$

Solution Steps

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

$$y=\frac{1}{4}\left(x^{2}-6x+9\right)-1$$

Use the distributive property to multiply \frac{1}{4} by x^{2}-6x+9.

$$y=\frac{1}{4}x^{2}-\frac{3}{2}x+\frac{9}{4}-1$$

Subtract 1 from \frac{9}{4} to get \frac{5}{4}.

$$y=\frac{1}{4}x^{2}-\frac{3}{2}x+\frac{5}{4}$$

Solve for x (complex solution)

$$x=-2\sqrt{y+1}+3$$

$$x=2\sqrt{y+1}+3$$

Solve for x

$$x=-2\sqrt{y+1}+3$$

$$x=2\sqrt{y+1}+3\text{, }y\geq -1$$