Answer
See explanation
Work Step by Step
Finding the quadratic function in standard form $f(x)=a(x-h)^2+k$:
$$f(x)=x^2+12x+40$$ $$f(x)=x^2+12x+\left(\frac{12}{2}\right)^2+40-\left(\frac{12}{2}\right)^2$$ $$f(x)=x^2+12x+36+40-36$$ $$f(x)=(x+6)^2+4$$
The sketch of the graph of the function is as shown.
Notice that the vertex is: $$(-6,4)$$
The axis of symmetry is: $$x=-6$$
There is no $x$-intercept.
