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Chapter 3: Problem 16

Find the coordinates of the vertex for the parabola defined by the given quadratic function. $$f(x)=-2 x^{2}+8 x-1$$

Short Answer

Expert verified
The coordinates of the vertex for the given parabola are (2, 11).

Step by step solution

01

Calculate the x-coordinate of the vertex

The x-coordinate of the vertex, denoted as \(h\), is given by the formula \(h = -b/(2a)\). In the given function \(f(x)=-2x^{2}+8x-1\), \(a = -2\) and \(b = 8\). Substituting these values into the formula, we get \(h = -8/(2*-2) = 2\)
02

Calculate the y-coordinate of the vertex

Once we know the x-coordinate of the vertex (h=2), we can find the y-coordinate, denoted as \(k\), by substituting \(h\) into the function. Therefore, \(k = f(2) = -2(2)^2 + 8*2 - 1 = -4 + 16 - 1 = 11\)
03

Present the final Answer

The vertex of the parabola defined by the function \(f(x)=-2x^{2}+8x-1\) is at point (2, 11).

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