Here are the graphs of , , and .

1. How do the 3 graphs compare?

   

   Three parabolas in x y plane, origin O. X axis negative 10 to 4, by 2’s. Y axis negative 12 to 12, by 4s. First parabola labeled y equals x squared opens upward with vertex at the origin. Second parabola labeled y equals x squared minus 5 opens upward with a vertex at 0 comma negative 5. Third parabola labeled y equals open parenthesis, x plus 2, end parenthesis, squared, minus 8 opens upward with a vertex at negative 2 comma negative 8.

2. Compare the graphs of and . What role does the -5 play in the comparison?
3. Compare the graphs of and  . What role do the 2 and 8 play in the comparison?
   

Select all the equations with a graph whose vertex has both a positive -coordinate and a positive -coordinate.

The height, in feet, of a soccer ball is modeled by the equation , where time, , is measured in seconds after it was kicked.

1. How far above the ground was the ball when kicked?
2. What was the initial upward velocity of the ball?
3. Why is the coefficient of the squared term negative?