Question

Two equations and their graphs are given. Find the intersection point(s) of the graphs by solving the system. X2 + y = 0 x3 − 12x − y = 0 (x, y) = ( ) (smaller x-value) (x, y) = ( ) (x, y) = ( ) (larger x-value)

Answer 1

Given

x² +y = 0

x³ -12x -y = 0

Find

the intersection point(s) (x, y)

Solution

Add the two equations together, then factor.

... (x² +y) + (x³ -12x -y) = 0 + 0

... x³ +x² -12x = 0

... x(x +4)(x -3) = 0

Then x = {0, -4, 3}.

The corresponding y-values are

... y = -x² = {0, -16, -9}

The points of intersection are (-4, -16), (0, 0), (3, -9)