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Chapter 3: Problem 9

Find the coordinates of the vertex for the parabola defined by the given quadratic function. $$f(x)=2(x-3)^{2}+1$$

Short Answer

Expert verified
The vertex coordinates of the parabola defined by the function \(f(x)=2(x-3)^{2}+1\) are (3, 1).

Step by step solution

01

Identify the quadratic function form

Recognize that the given function \(f(x)=2(x-3)^{2}+1\) is written in the vertex form of a quadratic function, that is \(f(x) = a(x-h)^2 + k\).
02

Identify h

Identify the value of 'h' in the given function. 'h' is the number subtracted from x inside the parenthesis. Here in \(f(x)=2(x-3)^{2}+1\), the 'h' value is 3.
03

Identify k

Identify the value of 'k' in the given function. 'k' is the number added or subtracted outside the parenthesis. Here in \(f(x)=2(x-3)^{2}+1\), the k value is 1.
04

Write down the vertex coordinates

The vertex form of the quadratic function already gives the coordinates for the vertex of the parabola. Therefore, the vertex coordinates for the given function are (h, k) or (3, 1).

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