Find X-Axis Intersections of y = x² + 4: Quadratic Function Analysis

Determine the points of intersection of the function

$y=x^2+4$

With the X

To determine the intersection points of the function $y = x^2 + 4$ with the x-axis, we set the equation to zero, i.e., find where $x^2 + 4 = 0$.

Let's solve the equation:

• $x^2 + 4 = 0$
• Subtract 4 on both sides: $x^2 = -4$
• Since $x^2 = -4$ has no real solutions (the square of a real number cannot be negative), there are no real $x$-intercepts.

Therefore, the parabola defined by $y = x^2 + 4$ does not intersect the x-axis.

The solution to the problem is No solution.