Questions: Consider the following function. t(x)=(x-2)^2-9 Find the vertex.

Transcript text: Consider the following function. \[ t(x)=(x-2)^{2}-9 \] Find the vertex.

Solution

Step 1: Identify the form of the quadratic function

The given function is \( f(x) = (x - 2)^2 - 9 \). This is in the vertex form of a quadratic function, which is \( f(x) = a(x - h)^2 + k \).

Step 2: Determine the vertex

In the vertex form \( f(x) = a(x - h)^2 + k \), the vertex is given by the point \((h, k)\). Here, \( h = 2 \) and \( k = -9 \).

The vertex of the function \( f(x) = (x - 2)^2 - 9 \) is \((2, -9)\).

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