Answer
(a) $y=-0.0082833093{{x}^{2}}+0.8242996891x+0.2121786608$
(b) $17.325 feet$ .
Work Step by Step
(a)
Use the TI-83 calculator and proceed as follows,
Step 1: Press ON key.
Step 2: Press STAT key.
Step 3: Select Edit.
Step 4: Enter the values of the ordered pairs under L1 and L2.
Step 5: Press STAT key.
Step 6: Select Calc.
Step 7: Press QuadReg and press enter; it shows the values of a, b and c.
$\begin{align}
& y=a{{x}^{2}}+bx+c \\
& a=-0.0082833093 \\
& b=0.8242996891 \\
& c=0.2121786608
\end{align}$
Thus, the quadratic function is $y=-0.0082833093{{x}^{2}}+0.8242996891x+0.2121786608$.
(b)
$y=-0.0082833093{{x}^{2}}+0.8242996891x+0.2121786608$
To find the depth of the river 70 feet from the bank, substitute $x=70$ in the function
$y=-0.0082833093{{x}^{2}}+0.8242996891x+0.2121786608$.
That is,
$\begin{align}
& y=-0.0082833093{{x}^{2}}+0.8242996891x+0.2121786608 \\
& =-0.0082833093{{\left( 70 \right)}^{2}}+0.8242996891\left( 70 \right)+0.2121786608 \\
& \approx 17.325
\end{align}$
Thus, the depth of the river 70 feet from the bank of the river is $17.325 feet$.
