Answer
The graph is shown below:
Work Step by Step
Let us consider the parabola defined by the quadratic equation $f\left( x \right)=0.01{{x}^{2}}+0.6x+100$.
The coefficient of ${{x}^{2}}$ is $0.01$.
Therefore, the value of $a$ is positive and the parabola would be opening upwards.
Compare the equation with the standard form of the quadratic equation $f\left( x \right)=a{{x}^{2}}+bx+c$.
So,
$\begin{align}
& a=0.01 \\
& b=0.6 \\
& c=100
\end{align}$
The general form of the parabola vertex is $\left( -\frac{b}{2a},f\left( -\frac{b}{2a} \right) \right)$.
Putting in the values of $a$ and $b$ to find the $x\text{-}$ coordinate of the vertex, we get:
$\begin{align}
& x=-\frac{b}{2a} \\
& =-\frac{0.6}{2\left( 0.01 \right)} \\
& =-\frac{600}{20} \\
& =-30
\end{align}$
Putting in the value of $x$ in the equation to find the $y\text{-}$ coordinate of the vertex, we get:
$\begin{align}
& f\left( x \right)=0.01{{x}^{2}}+0.6x+100 \\
& f\left( 30 \right)=0.01{{\left( -30 \right)}^{2}}+0.6\left( -30 \right)+100 \\
& =9-18+100 \\
& =91
\end{align}$
Thus, the vertex of the parabola is $\left( -\frac{b}{2a},f\left( -\frac{b}{2a} \right) \right)=\left( -30,91 \right)$.
Use a graphing utility to plot the graph:
Step 1: Write the function.
Step 2: Set the window $x:\left( -250,250,60 \right)$ and $y:\left( 0,400,30 \right)$.
Step 3: Plot the graph.
