The family of curves given by y = k(x - a)(x - b) is a representation of:

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Question: The family of curves given by y = k(x - a)(x - b) is a representation of:

Options:

Correct Answer: Quadratic functions

Solution:

The equation y = k(x - a)(x - b) represents a family of quadratic functions.

The family of curves given by y = k(x - a)(x - b) is a representation of:

The family of curves given by y = k(x - a)(x - b) is a representation of:

Step 1: Identify the equation given, which is y = k(x - a)(x - b).
Step 2: Recognize that this equation is in the form of a quadratic function, which generally looks like y = Ax^2 + Bx + C.
Step 3: Note that 'k' is a constant that affects the vertical stretch or compression of the curve.
Step 4: Understand that 'a' and 'b' are constants that determine the x-intercepts of the curve.
Step 5: Conclude that since the equation is quadratic and can take different values of 'k', 'a', and 'b', it represents a family of curves.

Quadratic Functions – The equation represents a family of quadratic functions, which are parabolas defined by the roots at x = a and x = b.