Question

Steve and Ed stand next to each other and throw footballs in the air. The path of Steve’s football is described by the equation y = –2x^2 + 5x + 4. The path of Ed’s football is shown by the graph.




In each function, x is the horizontal distance the football travels in meters, and y represents the height.

Whose football reaches a greater height?
A. Steve’s football
B. Ed’s football
C. Both footballs reach the same height.

Answer 1

Th question is clearly asking for the maximum value of both the functions, that is, the vertex of each function.

The path of Ed’s football is shown by the graph clearly shows the coordinates of the vertex (the maximum value of the graph). 

That is;

              (h,k) = (1.5 , 7.5)

(h,k) represents the coordinates of the vertex.

On the other hand, The path of Steve’s football is described by the equation:
               
               y = - 2x² + 5x + 4

Using the equation of symmetry:

               x = - b ÷ 2a
Where,

a = -2

b = 5

Therefore,

               x = - 5 ÷ - 4

               x = 5 / 4

               x = 1.25

Substituting the value of x into the main equation to get the y-value.

               y = - 2x² + 5x + 4

               y = - 2(1.25)² + 5(1.25) + 4

               y = - 3.125 + 6.25 + 4

               y = 7.125

Hence, the vertex (h,k) = (1.25 , 7.125)

From the above results, Ed’s football reaches a greater height.