[填空题]
A healthcare company/. k:vhi)nuy,q dpovl2x v )1g 4ttav;4zr hpo9igx/ 24j7hiois designing a new deodorant stick that can be modelled by the shape of a parabola as the top, 4go ij;4a74thp2o 9v/tx zrihvertical lines as the sides and a horizontal line as the base, on the x -axis. The parabola has end points at (0,7) and (5,7) , and vertex at (2.5,8) .
This design is shown in the diagram below. All distances are measured in centimetres.
The quadratic curve can be expressed in the form y=$a x^{2}+b x+c$ for $0 \leq x \leq 5$ .
1. 1. Find the value of c is .
2. Using the points (2.5,8) and (5,7) , write two equations in a and b .
3. Hence, find the equation of the quadratic curve; we get y=-ax$^2$+bx+c;a= ,b= ,c= .
2. Find the area of the shaded region in the deodorant design.
