How many common points have the graphs of the functions Y = x ^ 2 + 5x and y = -6

Two functions are given. You need to find the intersection points.

To find the points of intersection of the graphs of two functions, it is necessary to equate the right parts.

y1 = x ^ 2 + 5 * x;

y2 = 6;

We equate the right-hand sides of the equalities, find x and get the intersection points.

x ^ 2 + 5 * x = 6;

x ^ 2 + 5 * x – 6 = 0;

D = 25 – 4 * (-6) = 49;

x1 = (-5 + 7) / 2 = 1;

x2 = (-5 – 7) / 2 = -6;

We get two values of x – respectively, two points of intersection of the graphs. The values of the ordinates of the intersection points can only be equal to 6, even based on the second function.

We get two points – (1; 6) and (-6; 6).