Convert the equation to vertex form

Question

The path of a freestyle skier’s reverse somersault can be illustrated by the graph of the function h= -5t^2 + 10t + 3, where h is the height, in meters above the ground and t is time, in seconds, after the skier leaves the ski jump.

a. Rough sketch the graph of the skiers height and fime

b. What is the height of the skier at 1.5 seconds?

c. Convert the equation to “vertex form”

d. The skier’s maximum height occurs at ____ when the time is____

e. When does the skier make contact with the ground?

Answer 1

y = -5t² +10t +3

This is in standard form.

To convert to vertex form ,

y = -5 (t² - 2t) +3

= -5 [(t² -2t +1 -1)] +3

= -5[(t-1)² -1] + 3

= -5(t-1)² +5 +3

= -5(t-1)² +8