Solve y=-4(x-5)^2-3

$$y = - 4 ( x - 5 ) ^ { 2 } - 3$$

Solve for y

$$y=-4\left(x-5\right)^{2}-3$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-5\right)^{2}.

$$y=-4\left(x^{2}-10x+25\right)-3$$

Use the distributive property to multiply -4 by x^{2}-10x+25.

$$y=-4x^{2}+40x-100-3$$

Subtract 3 from -100 to get -103.

$$y=-4x^{2}+40x-103$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{-y-3}}{2}+5$$

$$x=\frac{\sqrt{-y-3}}{2}+5$$

Solve for x

$$x=-\frac{\sqrt{-y-3}}{2}+5$$

$$x=\frac{\sqrt{-y-3}}{2}+5\text{, }y\leq -3$$