we have the equation
[tex]h(x)=-0.3(x-10)^2-6[/tex]
this is a vertical parabola open downward (because the leading coefficient is negative)
Part 1
the vertex represents a maximum
the vertex is the point (10,-6)
Part 2
Vertical intercept
For x=0
h(x)=-0.3(0-10)^2-6
h(x)=-36
the vertical intercept is (0,-36)
Part 3
Horizontal intercepts
For h(x)=0
[tex]\begin{gathered} 0=-0.3(x-10)^2-6 \\ -0.3(x-10)^2=6 \\ (x-10)^2=-20 \end{gathered}[/tex]
the graph has no real horizontal intercepts (complex numbers)
horizontal intercepts --------> DNE
see the attached figure to better understand the problem
