Find the coordinates of the points of intersection of this graph y = x ^ 2 + 2x-3 with the graph of the function y = 7x + 63.

1. Let’s equate the functions to each other:

y = x ^ 2 + 2x – 3;
y = 7x + 63;
x ^ 2 + 2x – 3 = 7x + 63.
2. Move everything to the left side, change the signs, and give similar terms:

x ^ 2 + 2x – 3 – 7x – 63 = 0;
x ^ 2 – 5x – 66 = 0;
D = b ^ 2 – 4ac;
D = 5 ^ 2 – 4 * 1 * (-66) = 25 + 264 = 289;
x = (-b ± √D) / 2a;
x = (5 ± √289) / 2 = (5 ± 17) / 2;
1) x = (5 – 17) / 2 = -12/2 = -6;

y = 7x + 63 = 7 * (-6) + 63 = -42 + 63 = 21;

2) x = (5 + 17) / 2 = 22/2 = 11;

y = 7x + 63 = 7 * 11 + 63 = 77 + 63 = 140;

Answer: (-6; 21), (11; 140).