Calculate the coordinates of the intersection points of the graphs of the functions y = x2-4 and y = x + 2 A. (-2; 0) and (3; 5)

Calculate the coordinates of the intersection points of the graphs of the functions y = x^2-4 and y = x + 2 A. (-2; 0) and (3; 5) B. (-2; 3) and (0; 5) C. (-2; 0) and (5; 3) D. (3; 5) and (0; -2)

To find the coordinates of the intersection points of the graphs of the functions y = x ^ 2 – 4 and y = x + 2, you need to equate the right sides of the equations and find the abscissas of the intersection points. Then substitute the abscissa values into any of the equations and find the corresponding ordinates.

1) Find the abscissas of the intersection points.

x ^ 2 – 4 = x + 2;

x ^ 2 – 4 – x – 2 = 0;

x ^ 2 – x – 6 = 0;

D = b ^ 2 – 4ac;

D = (-1) ^ 2 – 4 * 1 * (-6) = 1 + 24 = 25; √D = 5;

x = (-b ± √D) / (2a);

x1 = (1 + 5) / 2 = 6/2 = 3;

x2 = (1 – 5) / 2 = -4/2 = -2.

2) Find the ordinates of the intersection points.

y1 = x1 ^ 2 – 4;

y1 = 3 ^ 3 – 4 = 9 – 4 = 5;

y2 = x2 ^ 2 – 4;

y2 = (-2) ^ 2 – 4 = 4 – 4 = 0.

Answer. (3; 5); (-twenty).