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Chapter 2: Problem 15

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

Short Answer

Expert verified
The coordinates of the vertex for the given quadratic function are \((1,5)\).

Step by step solution

01

Compute the x-coordinate of the vertex

First calculate the x-coordinate of the vertex, represented by \(h\). This can be found using the formula \(h = -b / 2a\), where \(b = -2\) and \(a = -1\). Thus, \(h = --2 / (2*-1) = 1\).
02

Compute the y-coordinate of the vertex

Next, calculate the y-coordinate of the vertex, represented by \(k\). This is simply the value of the function at the x-coordinate of the vertex, or \(f(h)\). Thus, \(k = f(1) = -1^2 - 2*1 + 8 = 5\).
03

State the coordinates of the vertex

Finally, state the coordinates of the vertex. Since the x- and y-values represent a coordinate point, they can be combined to form the vertex: \((1,5)\).

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