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Chapter 3: Problem 11

Find the coordinates of the vertex for the parabola defined by the given quadratic function. $$f(x)=-2(x+1)^{2}+5$$

Short Answer

Expert verified
Therefore, the coordinates of the vertex for the given parabola are \((-1,5)\).

Step by step solution

01

Identify the Form of the Quadratic Function

The given quadratic function is in the form \(f(x)=a(x-h)^{2}+k\), where \(h\) is the x-coordinate and \(k\) is the y-coordinate of the vertex. This form of the quadratic function is generally called the vertex form. The quadratic function given is \(f(x)=-2(x+1)^{2}+5.\)
02

Find the x-coordinate of the Vertex

In the given quadratic function, \(-1\) is subtracted from \(x\), which means that the x-coordinate of the vertex is \(-1\). In general, the x-coordinate of the vertex \(h\) is the value that makes the squared term equal to zero. Thus, \(h = -1\).
03

Find the y-coordinate of the Vertex

The y-coordinate of the vertex \(k\) is the constant in the given quadratic function, which is \(5\) in this case. Thus, \(k = 5\).

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