Y=0.5x^2-8

Solution for Y=0.5x^2-8 equation:

=0.5Y^2-8

We move all terms to the left:

-(0.5Y^2-8)=0

We get rid of parentheses

-0.5Y^2+8=0

a = -0.5; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-0.5)·8
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4}{2*-0.5}=\frac{-4}{-1}
=+4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4}{2*-0.5}=\frac{4}{-1}
=-4
$