Functions (Grade 12 NSC Matric Mathematics): Flashcards

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Quadratic Functions
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Inverse of y=ax2y = ax^2

y=±xay = \pm\sqrt{\frac{x}{a}}

Method to find inverse function

Switch x and y, then solve for y

Why ± in inverse of quadratic

Two branches: positive and negative

Domain and range in inverse functions

They switch roles

Vertical line test purpose

Check if relation is a function

Why y=±xay = \pm\sqrt{\frac{x}{a}} fails vertical line test

Two y-values for each x-value

Making inverse of quadratic a function

Restrict domain of original function

Inverse of y=ax2y = ax^2 for x≥0x \geq 0

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

Line of reflection for inverse graphs

y=xy = x

Point (a,b)(a,b) on function becomes on inverse

(b,a)(b,a)

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