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

Question

Determine the points of intersection of the function

$y=x^2+4$

With the X

00:00 Find the intersection point of the function with the X-axis

00:03 At the intersection point with the X-axis, Y equals 0

00:07 Substitute Y=0 in our equation and solve for the intersection point:

00:13 Isolate X

00:19 Any number squared is necessarily positive

00:40 Therefore there is no intersection point with the X-axis

00:44 And this is the solution to the question

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.

No solution