Gr12 Mathematics: Ch 2.4 Quadratic Functions

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What is the first step to find the inverse of a quadratic function y = ax^2?

Express the new equation in function notation

Solve for x

Restrict the domain

Interchange x and y in the equation (correct)

What is the domain of the inverse function of y = ax^2 if a > 0?

x > 0

x ≥ 0 (correct)

All real numbers

x < 0

What is the range of the inverse function of y = ax^2 if a < 0?

y < 0

All real numbers

y ≤ 0 (correct)

y > 0

What is the x-intercept of the graph of f(x) = -x^2?

x = 0 Signup and view all the answers

What is the equation of the inverse function of y = 2x^2?

y = √(x/2) Signup and view all the answers

What is a property of the inverse function of y = ax^2?

The domain and range are swapped Signup and view all the answers

What is the purpose of restricting the domain of a quadratic function?

To make the function one-to-one Signup and view all the answers

What is the relationship between the domain and range of a quadratic function and its inverse?

The domain of the original function becomes the range of the inverse function Signup and view all the answers

What is the y-intercept of the graph of the inverse function of y = -x^2?

y = 0 Signup and view all the answers

What is the equation of the inverse function of y = ax^2 if a < 0?

y = √(-x/a) Signup and view all the answers

What is the restriction on the domain of y = ax^2 if a > 0, in order to make its inverse a function?

x ≥ 0 Signup and view all the answers

What is a characteristic of the graphs of y = -x^2 and its inverse?

They are reflections of each other about the line y = x Signup and view all the answers

What is the main purpose of interchanging x and y in the equation y = ax^2 when finding its inverse?

To obtain the inverse function's equation Signup and view all the answers

What is the resulting equation after solving for y in the inverse function of y = ax^2?

y = ±√(x/a) Signup and view all the answers

What is the relationship between the domain of the original function of y = ax^2 and the range of its inverse function?

The domain of the original function becomes the range of the inverse function Signup and view all the answers

Why is it necessary to restrict the domain of a quadratic function in some cases?

To make its inverse a function Signup and view all the answers

What is a characteristic of the graphs of y = -x^2 and its inverse?

They are reflections about the line y = x Signup and view all the answers

What is the y-intercept of the graph of the inverse function of y = ax^2?

0 Signup and view all the answers

Gr12 Mathematics: Ch 2.4 Quadratic Functions

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Questions and Answers

What is the first step to find the inverse of a quadratic function y = ax^2?

What is the domain of the inverse function of y = ax^2 if a > 0?

What is the range of the inverse function of y = ax^2 if a < 0?

What is the x-intercept of the graph of f(x) = -x^2?

What is the equation of the inverse function of y = 2x^2?

What is a property of the inverse function of y = ax^2?

What is the purpose of restricting the domain of a quadratic function?

What is the relationship between the domain and range of a quadratic function and its inverse?

What is the y-intercept of the graph of the inverse function of y = -x^2?

What is the equation of the inverse function of y = ax^2 if a < 0?

What is the restriction on the domain of y = ax^2 if a > 0, in order to make its inverse a function?

What is a characteristic of the graphs of y = -x^2 and its inverse?

What is the main purpose of interchanging x and y in the equation y = ax^2 when finding its inverse?

What is the resulting equation after solving for y in the inverse function of y = ax^2?

What is the relationship between the domain of the original function of y = ax^2 and the range of its inverse function?

Why is it necessary to restrict the domain of a quadratic function in some cases?

What is a characteristic of the graphs of y = -x^2 and its inverse?

What is the y-intercept of the graph of the inverse function of y = ax^2?

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