Y=0.5x2-1

Solution for Y=0.5x2-1 equation:

=0.5Y^2-1

We move all terms to the left:

-(0.5Y^2-1)=0

We get rid of parentheses

-0.5Y^2+1=0

a = -0.5; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-0.5)·1
Δ = 2
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-\sqrt{2}}{2*-0.5}=\frac{0-\sqrt{2}}{-1}
=-\frac{\sqrt{}}{-1}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+\sqrt{2}}{2*-0.5}=\frac{0+\sqrt{2}}{-1}
=\frac{\sqrt{}}{-1}
$