Rewrite the equation in standard form, then find the vertex of the graph of \( f(x) \). \( f(x)=x^{2}-10 x+23 \). In standard form, \( f(x)=(x-5)^{2}-2 \) The vertex is at

First, let’s highlight the vertex directly derived from the standard form. In your rewritten equation \( f(x) = (x-5)^{2} - 2 \), the vertex is at the point where the squared term becomes zero, which occurs at \( x = 5 \). This means the coordinates of the vertex are \( (5, -2) \). The transformation of the equation into standard form not only showcases the vertex beautifully but also helps to visualize the parabola's direction and the position of the vertex relative to the axis of symmetry, which is crucial in graphing and understanding its shape.