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Chapter 2: Problem 14

Find the coordinates of the vertex for the parabola defined by the given quadratic function. $$f(x)=3 x^{2}-12 x+1$$

Short Answer

Expert verified
The vertex of the parabola defined by the function \(3x^{2}-12x+1\) is located at (2, -7).

Step by step solution

01

- Calculating the x-coordinate 'h'

First find the x-coordinate of the vertex using the formula \(h= -b/2a\). For the given equation \(f(x)=3x^{2}-12x+1\), a = 3 and b = -12, resulting in \(h = -(-12)/2(3)=2\).
02

- Calculating the y-coordinate 'k'

Now that the x-coordinate 'h' is found, plug it into the function to find the y-coordinate 'k', which results in \[f(2)=3(2)^{2}-12(2)+1=-7.\] This is the y-coordinate of the vertex.
03

- Present the Vertex

As the coordinates for the vertex h and k are already found as h = 2 and k = -7, the vertex of the parabola can be written as (h, k) = (2, -7).

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