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Chapter 3: 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 vertex of the parabola is at the coordinates (1, 5).

Step by step solution

01

Identify the coefficients

For the given function \(f(x) = -x^{2} -2x + 8\), the coefficients are \(a=-1\), \(b=-2\), and \(c=8\).
02

Calculate the x-coordinate of the vertex

Use the formula \(h = -b/2a\) to calculate the x-coordinate of the vertex. So, \(h = --2/ 2(-1) = 1\).
03

Calculate the y-coordinate of the vertex

Substitute the x-coordinate (1) into the quadratic function to calculate the y-coordinate of the vertex. Thus, \(k = f(1) = -(1)^{2} -2(1) +8 = 5\).

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