Find the intersection points of the graphs of the functions y = -3x ^ 2 and y = 3x

In order to find the intersection points of the graphs of the functions given by the equations y = -3x ^ 2 and y = 3x, we will solve a system of these equations.

System of equations:

y = -3x ^ 2;

y = 3x.

We solve the system using the substitution method. Let’s substitute in the first equation instead of y the expression from the second equation.

3x = -3x ^ 2;

y = 3x.

We solve the first equation of the system.

3x = -3x ^ 2;

3x – 3x ^ 2 = 0;

3x (1 – x) = 0.

The solution to the equation are the numbers:

3x = 0; x = 0;

1 – x = 0; x = 1.

A collection of systems.

System 1:

x = 0;

y = 3 * 0 = 0;

System 2:

x = 1;

y = 3 * 1 = 3.

Answer: (0; 0) and (1; 3).