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Chapter 2: Problem 12

Find the coordinates of the vertex for the parabola defined by the given quadratic function. $$f(x)=-2(x+4)^{2}-8$$

Short Answer

Expert verified
The vertex's coordinates of the parabola defined by the quadratic function are \((4, -8)\).

Step by step solution

01

Identify the Vertex form of a Quadratic Function

The vertex form of a quadratic function \(f(x)\) is \(f(x)=a(x-h)^{2}+k\) where \((-h, k)\) are the coordinates of the vertex and \(a\) is the stretching factor. This form gives us a direct way to identify the vertex if our given function is in this format.
02

Compare Given Function with the Vertex Form

Our given function is \(f(x)=-2(x+4)^{2}-8\). Here, we can identify \(a=-2\), \(h=-4\) and \(k=-8\). As per the details from the vertex form, the generators of the vertex are \((-h, k)\)
03

Identify the Vertex

As the vertex's coordinates are \((-h, k)\), substituting our values, we'll have \((-(-4), -8)\), and that simplifies down to \((4, -8)\).

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Most popular questions from this chapter

Write the equation of a rational function \(f(x)=\frac{p(x)}{q(x)}\) having the indicated properties, in which the degrees of p and q are as small as possible. More than one correct function may be possible. Graph your function using a graphing utility to verify that it has the required properties. \(f\) has a vertical asymptote given by \(x=1,\) a slant asymptote whose equation is \(y=x, y\) -intercept at \(2,\) and \(x\)-intercepts at -1 and 2.

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