Question

what are the coordinates of the vertex of the function $f(x)=x^2 - 8x + 23$? enter your answers in the boxes. the vertex is $(square,square)$.

Explanation:

Step1: Find x-coordinate of vertex

For quadratic $f(x)=ax^2+bx+c$, $x = -\frac{b}{2a}$. Here $a=1, b=-8$:
$x = -\frac{-8}{2\times1} = 4$

Step2: Find y-coordinate of vertex

Substitute $x=4$ into $f(x)$:
$f(4) = 4^2 - 8\times4 + 23 = 16 - 32 + 23 = 7$

Answer:

$(4, 7)$