Determine the family of curves represented by the equation y = kx^2, where k is

Determine the family of curves represented by the equation y = kx^2, where k is a constant.

Determine the family of curves represented by the equation y = kx^2, where k is a constant.

Correct Answer: y = kx^2 represents a family of parabolas.

Step 1: Identify the equation given, which is y = kx^2.
Step 2: Recognize that 'k' is a constant that can take different values.
Step 3: Understand that when k is positive (k > 0), the parabola opens upwards.
Step 4: Understand that when k is negative (k < 0), the parabola opens downwards.
Step 5: Note that for different values of k, you get different parabolas, but they all have the same basic shape.
Step 6: Conclude that the equation y = kx^2 represents a family of parabolas based on the value of k.

Quadratic Functions – The equation y = kx^2 represents quadratic functions, specifically parabolas, where the value of k determines the width and direction of the parabola.
Family of Curves – The term 'family of curves' refers to a set of curves that share a common form but differ based on the parameter k.
Graphical Interpretation – Understanding how the value of k affects the graph's shape and orientation is crucial for visualizing the family of curves.