$\backslash$table$[[$Wind Speed $x,mph,14,22,30,38,46],[$Power $y,W,320,490,540,500,480]]$

Use quadratic splines interpolation with the data in Problem $1$ to calculate the power at the following wind speeds: $($a$)24$ mph and $($b$)35$ mph $.$ For this problem, perform the calculations in MATLAB.

Start a new MATLAB script and save it as quadInterp.m$.$ At the beginning of the script, create vectors $x$ and $y$ with the data points. pts

Plot the data points. $0\mathrm{.}1$ pts s

Open a new figure $($ise command figure$).$

Plot $y$ versus $x.$ Use solid red circles for each data point and set the line width to $2.$

Label the axes and give the figure a title.

Set the font size of the current axes of the figure to $16.$ Use set$$gca$,$ 'fontsize', $16.$

There are $5$ data points and therefore $4$ splines. The equation for each spline is

$f_i(x)=a_i{r}^2+b_{i}x+c_i,i=1,...,4.$

Write down the equations you need to solve in your homework report, like what we did in class. $[0\mathrm{.}4pts$

$4.$ Formulate the system of linear equations into a matrix form

$A*z=b$

Provide values of $A,b,$ and $z$ in your homework report. Solve for $z$ using the backslash command in MATLAB. Provide the equations for the fitted quadratic splines in your homework report. $[0\mathrm{.}4$ pts $]$

$5.$ Plot the data points and the fitted polynomials against each other in a single plot. Include the plot in your homework report. What do you observe compared to linear splines interpolation? $[0\mathrm{.}4$ pts $]$

$6.$ Calculate the power at the following wind speeds: $($a$)24$ mph and $($b$)35$ mph $.$ Provide the values in your homework report. $[0\mathrm{.}1$ pts