Answer
See explanation
Work Step by Step
Finding the quadratic function in standard form $f(x)=a(x-h)^2+k$:
$$f(x)=x^2-8x+21$$
$$f(x)=x^2-8x+\left(\frac{-8}{2}\right)^2+21-\left(\frac{-8}{2}\right)^2$$
$$f(x)=x^2-8x+16+21-16$$
$$f(x)=(x-4)^2+5$$
The sketch of the graph of the function is as shown.
Notice that the vertex is:
$$(4,5)$$
The axis of symmetry is:
$$x=4$$
There is no $x$-intercept.
