Final answer:
Find intersection points, calculate rectangle and triangle areas, then sum for total shaded region area between parabola and dashed line. The answer is not mentioned in the options.
Step-by-step explanation:
To determine the area of the shaded region between the solid parabola and the dashed line, we need to find the points of intersection between the two equations. Set y = x2 - 14 equal to y = 13x:
x2 - 14 = 13x
Bringing all terms to one side, we get x2 - 13x - 14 = 0
Factoring the quadratic equation, we have (x - 14)(x + 1) = 0. So x = 14 or x = -1.
Substituting these values back into y = x2 - 14, we find that the corresponding y-values are y = 142 - 14 = 182 and y = (-1)2 - 14 = -13.
Therefore, the points of intersection are (14, 182) and (-1, -13). The shaded region between the parabola and the line can be divided into a rectangle and a triangle. The area of the rectangle is given by the product of the base length (14 - (-1) = 15) and the height (13) which equals 195. The area of the triangle is given by the base length (14 - (-1) = 15) multiplied by one-half the height (182 - (-13) = 195), which equals 1462.5. Adding the areas of the rectangle and the triangle, we get 195 + 1462.5 = 1657.5 square units.