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?

  • 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 &lt; 0
  • All real numbers
  • y ≤ 0 (correct)
  • y &gt; 0

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

<p>x = 0 (A)</p> Signup and view all the answers

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

<p>y = √(x/2) (C)</p> Signup and view all the answers

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

<p>The domain and range are swapped (B)</p> Signup and view all the answers

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

<p>To make the function one-to-one (D)</p> Signup and view all the answers

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

<p>The domain of the original function becomes the range of the inverse function (B)</p> Signup and view all the answers

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

<p>y = 0 (B)</p> Signup and view all the answers

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

<p>y = √(-x/a) (C)</p> 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?

<p>x ≥ 0 (C)</p> Signup and view all the answers

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

<p>They are reflections of each other about the line y = x (C)</p> 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?

<p>To obtain the inverse function's equation (C)</p> Signup and view all the answers

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

<p>y = ±√(x/a) (D)</p> 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?

<p>The domain of the original function becomes the range of the inverse function (D)</p> Signup and view all the answers

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

<p>To make its inverse a function (C)</p> Signup and view all the answers

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

<p>They are reflections about the line y = x (D)</p> Signup and view all the answers

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

<p>0 (B)</p> Signup and view all the answers

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