Question: The family of curves defined by the equation y = a(x - h)^2 + k represents which type of function?
Options:
Linear
Quadratic
Cubic
Rational
Correct Answer: Quadratic
Solution:
The equation y = a(x - h)^2 + k represents a quadratic function in vertex form.
The family of curves defined by the equation y = a(x - h)^2 + k represents which
Practice Questions
Q1
The family of curves defined by the equation y = a(x - h)^2 + k represents which type of function?
Linear
Quadratic
Cubic
Rational
Questions & Step-by-Step Solutions
The family of curves defined by the equation y = a(x - h)^2 + k represents which type of function?
Step 1: Identify the equation given, which is y = a(x - h)^2 + k.
Step 2: Notice that the equation has a squared term, (x - h)^2.
Step 3: Recognize that any equation with a variable squared (like x^2) is a quadratic function.
Step 4: Understand that this specific form, y = a(x - h)^2 + k, is called vertex form of a quadratic function.
Step 5: Conclude that the family of curves represented by this equation is indeed a quadratic function.
Quadratic Functions – Quadratic functions are polynomial functions of degree 2, typically represented in the form y = ax^2 + bx + c, and can also be expressed in vertex form as y = a(x - h)^2 + k.
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