Answer
See explanation
Work Step by Step
Using a graphing utility, the graph is as shown.
The vertex is $(3,0)$.
The axis of symmetry is $x=3$.
The $x$-intercept is $(3,0)$.
Finding the standard form of the quadratic function:
$$f(x)=-2x^2+12x-18$$ $$f(x)=-2(x^2-6x)-18$$ $$f(x)=-2\left(x^2-6x+\left(\frac{-6}{2}\right)^2\right)-18+2\left(\frac{-6}{2}\right)^2$$ $$f(x)=-2(x^2-6x+9)-18+18$$ $$f(x)=-2(x-3)^2$$
Thus, from the form $y=a(x-h)^2+k$, the vertex is $(3,0)$ and axis of symmetry is $x=3$.
Finding the $x$-intercept by setting $y=0$:
$$0=-2(x-3)^2$$ $$0=x-3$$ $$x=3$$
Thus, the $x$-intercept is $(3,0)$.
