# 3.3 The Inverse of a Quadratic Function

How to Find the Inverse of a Quadratic Function Example 4
How to Find the Inverse of a Quadratic Function Example 4

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3.3 The Inverse of a Quadratic Function
Given the function y = x2, what is the inverse function? x square it y x y 4 square it 16 16 4 – 4 square it 16 16 4 In order to obtain – 4 as part of the inverse, we must include y = and y =

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1- Sketch the graph of y = x2
3- Sketch the inverse of y = x2

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The inverse of y = x2 is not a function.
It does not pass the vertical line test One way to assure that the inverse will be a function is to limit the domain of y = x2.

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Example: Graph the relation y = x2, x ³ 0.
Equation of the inverse is The graph of is a function. Domain: x ³ 0 Range: y ³ 0

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Graph the relation y = x2, x £ 0. Equation of the inverse is The graph of is a function. Domain: x ³ 0 Range: y £ 0

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Determine the equation of the inverse.
Example: How can I restrict the domain of the function so that the inverse will be a function? y = (x + 2)2 + 1 The vertex is (– 2, 1) Domain: x ³ – 2 Range: y ³ 1 Determine the equation of the inverse.

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Example: Determine the vertex of the parabola
The method is called completing the square. y = 2×2 + 8x – 1 Factor the coefficient of x2 from the first two terms. Complete the square Remove the last term in parentheses Factor Vertex is (– 2, – 9)

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Sketch the graph of y = 2(x + 2)2 – 9 Domain:
How can we restrict the domain so that the inverse will be a function? Domain:

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Determine the equation of the inverse of:
y = 2(x + 2)2 – 9

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Example: Determine the vertex of the parabola
The method is called completing the square. y = – x2 + 6x + 2 Factor the coefficient of x2 from the first two terms. Complete the square Remove the last term in parentheses Factor vertex is (3, 11)

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Determine the equation of the inverse function
Determine the equation of the inverse function. Restrict the range of the inverse function so that it is also a function.

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