Find the coordinates of the points of intersection of the graph of the function y = √2 * x ^ 2-10x

Find the coordinates of the points of intersection of the graph of the function y = √2 * x ^ 2-10x + 8 * √2 with the coordinate axes.

1) Find the coordinates of the point of intersection with the oy axis. Oy axis equation: x = 0.

y = √2 * x ^ 2 – 10x + 8 * √2 = √2 * 0 ^ 2 – 10 * 0 + 8 * √2 = 0 – 0 + 8√2 = 8√2.

Answer. The point of intersection of the graph of the function y = √2 * x ^ 2 – 10x + 8 * √2 with the oy axis has coordinates (0; 8√2).

2) Find the coordinates of the points of intersection with the oh axis. Ox axis equation: y = 0.

√2 x ^ 2 – 10x + 8√2 = 0;

a = √2, b = – 10; c = 8√2;

D = b ^ 2 – 4ac;

D = (- 10) ^ 2 – 4 * √2 * 8√2 = 100 – 64 = 36; √D = 6;

x = (- b ± √D) / (2a);

x1 = (10 + 6) / (2 * √2) = 16 / 2√2 = 8 / √2;

x2 = (10 – 6) / 2√2 = 4 / 2√2 = 2 / √2

Answer. The points of intersection of the graph with the ox axis have coordinates (8 / √2; 0) and (2 / √2; 0).