Determine the family of curves represented by the equation y = ax^2 + bx + c.

Determine the family of curves represented by the equation y = ax^2 + bx + c.

Step 1: Identify the equation given, which is y = ax^2 + bx + c.
Step 2: Recognize that 'a', 'b', and 'c' are constants that can change.
Step 3: Understand that 'a' determines the direction and width of the parabola.
Step 4: Realize that 'b' affects the position of the vertex of the parabola.
Step 5: Know that 'c' represents the y-intercept of the parabola.
Step 6: Conclude that by changing the values of 'a', 'b', and 'c', you create different parabolas, forming a family of curves.

Quadratic Functions – The equation represents quadratic functions, which graph as parabolas.
Parameters of the Quadratic – The coefficients a, b, and c determine the shape, position, and orientation of the parabola.