(25 POINTS) Suppose you are tossing an apple up to a friend on a third-story balcony. After t seconds, the height of the apple, in feet, is given by h=-167² +38.41+0.96. Your friend catches the apple just as it reaches its highest point. How long does the apple take to
reach your friend, and at what height above the ground does your friend catch it?

Step-by-step explanation:

We assume your equation is intended to be ...

  h = -16t² +38.4t +0.96

The line of symmetry of this equation, hence the t-coordinate of the vertex, is given by ...

  h = ax² +bx +c

  t = -b/(2a) . . . . equation of the line of symmetry

  t = -38.4/(2(-16)) = 1.2

The friend catches the apple after 1.2 seconds.

The value of h at that point is ...

  t = (-16(1.2) +38.4)1.2 +0.96 = 19.2·1.2 +0.96 = 24

The apple is caught 24 feet above the ground.