Answer
See graph
Work Step by Step
The function that we want to graph is shown below. Follow the steps outline to graph the function. $$
h(x)=-0.3(x-10)^2-5.
$$ Step 1: We first determine the direction in which the function opens: The given function opens downward because the constant $a= -0.3$ is negative.
Step 2: Determine the vertex and the equation for the axis of symmetry. The vertex is $(10,-5)$ and the equation for the axis of symmetry is $x = 10$
Step 3: Find the $y$ and x intercepts. To find the $y$ intercept, set $x= 0$ to find the value of $y$. Similarly, to find the $x$ intercept, set $ y= 0$ to find the values of $x$.
$$
\begin{aligned}
h(0) & =-0.3(0-10)^2-5 \\
& =-0.3(100)-5 \\
& =-35.
\end{aligned}
$$ $y$-intercept: $(0,-35)$.
Set $ y = 0$ and solve. $$
\begin{aligned}
-0.3(x-10)^2-5 & =0 \\
-0.3(x-10)^2 & =5 \\
(x-10)^2 & =\frac{5}{-0.3} \\
(x-10)^2 & =-16.667.
\end{aligned}
$$ There is no $x$ intercept because we can't take the square root of a negative number.
Step 4: Find the domain and range of the function and sketch it.
Domain: All real numbers,
Range: $(-\infty, -5] $.
The graph of the parabola is shown in the figure.
