Solve y=-0,5(x-1,5)^2+1

$$y = - 0,5 ( x - 1,5 ) ^ { 2 } + 1$$

Solve for y

$$y=-\frac{\left(x-1,5\right)^{2}}{2}+1$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1,5\right)^{2}.

$$y=-0,5\left(x^{2}-3x+2,25\right)+1$$

Use the distributive property to multiply -0,5 by x^{2}-3x+2,25.

$$y=-0,5x^{2}+1,5x-1,125+1$$

Add -1,125 and 1 to get -0,125.

$$y=-0,5x^{2}+1,5x-0,125$$

Solve for x

$$x=-\sqrt{2-2y}+1,5$$

$$x=\sqrt{2-2y}+1,5\text{, }y\leq 1$$