What type of curves does the equation y = kx^2 represent?

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Question: What type of curves does the equation y = kx^2 represent?

Options:

Correct Answer: Parabolas with varying widths

Solution:

The equation y = kx^2 represents a family of parabolas that open upwards or downwards depending on the sign of \'k\'.

What type of curves does the equation y = kx^2 represent?

What type of curves does the equation y = kx^2 represent?

Step 1: Identify the equation given, which is y = kx^2.
Step 2: Recognize that this equation is in the form of a quadratic equation.
Step 3: Understand that a quadratic equation typically represents a curve called a parabola.
Step 4: Determine the role of 'k' in the equation. If 'k' is positive, the parabola opens upwards. If 'k' is negative, the parabola opens downwards.
Step 5: Conclude that the equation y = kx^2 represents parabolas that can either open upwards or downwards based on the value of 'k'.

No concepts available.