Question 761720
{{{y = (1/2)*x^2 + 4x - 2}}}

The key concept to remember is that for all points on the x axis, the y-coordinate is 0. i.e. y = 0 for all x on the x-axis.

At the point(s) where the parabola crosses the x axis, y will be 0.

In other words, {{{(1/2)*x^2 + 4x - 2 = 0}}}

Multiplying by 2 to get rid of the fraction in the left side

{{{x^2 + 8*x - 4 = 0}}}

This is a standard quadratic equation of the for ax^2 + bx + c = 0 with a = 1, b = 8 and c = -4.

We can solve it using the quadratic solver as shown below. The graph also shows the 2 points where the parabola intersects the x axis.

The two points where it crosses the x axis are (0.4721,0) and (-8.4721,0)

:)

*[invoke quadratic "x", 1, 8, -4]