Calculate the acute angle at which the parabola y = x ^ 2-4 intersects the abscissa axis.

Find the point of intersection of the parabola with the abscissa, for this we equate its equation to 0:

x ^ 2 – 4 = 0;

x ^ 2 = 4;

x1 = -2 and x2 = 2.

The intersection points were found 2. The tangent of the angle of inclination of the tangent to the graph at the point x0 can be easily found by the formula: tg (a) = f ‘(x0).

Let’s find the derivative of the function:

y ‘= (x ^ 2 – 4) = 2x.

Let’s calculate its value at the points x0 = -2 and x0 = 2:

y ‘(- 2) = 2 * (-2) = -4;

y (2) = 2 * 2 = 4.

Then the angles of inclination of the parabola are equal:

a1 = arctan (-4);

a2 = atctg (4).

Answer: angles arctg (-4) and atctg (4).