Question 136457
Your work so far is good!
But the x-intercepts are not right.
{{{y = x^2+2}}} Let y = 0.
{{{0 = x^2+2}}} subtract 2 from both sides.
{{{x^2 = -2}}} Take the square root of both sides.
{{{x = sqrt(-2)}}} and {{{x = -sqrt(-2)}}} or...
{{{x = sqrt(2)i}}} and {{{x = -sqrt(2)i}}}
As you can see, the x-intercepts are not real, meaning the parabola does not cross the x-axis.
Here's the graph of the equation:
{{{graph(400,400,-5,5,-3,8,x^2+2)}}}