Questions: In the following exercise, find the coordinates of the vertex for the parabola defined f(x)=3(x-5)^2+2 The vertex is (Type an ordered pair.)

Solution Steps

To find the vertex of a parabola given in the form \( f(x) = a(x-h)^2 + k \), we can directly identify the vertex as the point \((h, k)\). In this case, the function is already in vertex form, so we can read off the values of \(h\) and \(k\) from the equation.

The given function is \( f(x) = 3(x-5)^2 + 2 \). This is in the vertex form of a parabola, which is expressed as \( f(x) = a(x-h)^2 + k \), where \((h, k)\) represents the vertex.

From the equation, we can identify the values:

• \( h = 5 \)
• \( k = 2 \)

Thus, the coordinates of the vertex are \((5, 2)\).

Final Answer