Quadratic Functions (Grade 12 NSC Matric Mathematics): Quizzes

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Quadratic Functions
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What is the first step in finding the inverse of a quadratic function?

Interchange x and y

What is the inverse of y=ax2y = ax^2?

y=±xay = \pm\sqrt{\frac{x}{a}}

Why is the inverse of y=ax2y = ax^2 not automatically a function?

Two y-values for each x (± branches)

How do domain and range relate between a function and its inverse?

They switch roles

Why does y=±xay = \pm\sqrt{\frac{x}{a}} fail the vertical line test?

Vertical lines intersect at 2 points

If y=ax2y = ax^2 is restricted to x≥0x \geq 0, what is the inverse?

y=xay = \sqrt{\frac{x}{a}} for x≥0x \geq 0

What is the inverse of h(x)=3x2h(x) = 3x^2?

y=±x3y = \pm\sqrt{\frac{x}{3}}

Graphs of a function and its inverse are reflections across which line?

y=xy = x

For y=ax2y = ax^2 where a>0a > 0, what is the domain of the inverse?

x≥0x \geq 0

For f(x)=−x2f(x) = -x^2, when is −x\sqrt{-x} defined?

When x≤0x \leq 0

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