Set up and solve a system of equations to derive the coefficients of a quadratic polynomial. The polynomial is y=ax2+bx+c. It must pass through the points (1,4) and (4,1) and should have its minimum (zero slope) at x=5. The slope (s) of the quadratic is s=(2a)x+b. Construct and plot the polynomial over the interval 0 ≤ x ≤ 10.
Write a complete MATLAB script file that plots the curve. Add a title for the plot, and add labels for the horizontal and vertical axes. Make sure you provide enough points in your x vector to make a smooth curve. Include sufficient and appropriate comments.