height of a ball y(in feet) x seconds after it is thrown is given by the formula y=-16x^2+30x+5.5 use a graph to approximate the maximum height of the ball

Question

also find the vertex using Algebra to determine the maximum height of the ball

Answer 1

The graph of the height is a negative parabola.  The shape tells us that we will have a maximum height. 

 

y = -16x² + 30x + 5.5          can be rewritten as

 

y = -16x² + 30x + 11/2

 

 

From here, we can put this function in vertex form.  Vertex form is

 

y = a(x - h)² + k

 

where:

a is the coefficient of the x² term

The vertex has coordinates (h, k).  This vertex is your maximum.

 

 

y = -16(x² - (15/8)x + 225/256) + 313/16

 

y = -16(x - 15/16)² + 313/16

 

y = 16(x - 0.938)² + 19.563

 

 

The vertex is (0.938, 19.563).  Therefore, the maximum height is 19.563 feet.