Question

Jevonte kicks a football. Its height in feet is given by h = -16t² +48t where t

represents the time in seconds after kick. Interpret the coordinates of the vertex in
context.
The x-coordinate (or t-coordinate) of the vertex is
The y-coordinate (or h-coordinate) of the vertex is

Answer 1

The x-coordinate (or t-coordinate) of the vertex is 1.5 and represents how long the football has been in the air at its peak.

The y-coordinate (or h-coordinate) of the vertex is 36 and represents the football's height at its peak.

In Mathematics and Geometry, the maximum value of any function is a point on the graph where the function reaches its highest point. Additionally, the maximum value of Brett's quadratic function can be determined by finding the axis of symmetry;

Axis of symmetry, x = -b/2a

`h(t) = -16t^2 + 48t`

where:

a = -16, b = 48, and c = 0.

By substituting the values of a and b into the formula, we have;

Axis of symmetry, x = -48/2(-16)

Axis of symmetry, x = 48/32

Axis of symmetry, x = 1.5 hour.

Now, we can determine the maximum value (vertex) as follows;

`h(t) = -16t^2 + 48t\\\\h(1.5) = -16(1.5)^2 + 48(1.5)`

h(1.5) = 36 feet.