Real life Situations
Situation 1:
You and a friend are having a flour sack throwing competition. You throw a flour sack vertically upward from the ground. The equation to represent the flour sack's distance from the ground is y= -t² + 15t, y represents the distance and t represents the time.. How long will your flour sack remain in the air?
y= -t² + 15t
-b/ 2a -15/2 (-1)
-15/ -2 = 7.5
Solutions:
t ( -t+15)
t=0 -t+15 =0
( 0,0) (15, 0)
Your flour sack is in the air for 15 seconds.
-b/ 2a -15/2 (-1)
-15/ -2 = 7.5
Solutions:
t ( -t+15)
t=0 -t+15 =0
( 0,0) (15, 0)
Your flour sack is in the air for 15 seconds.
Your friends flour sack remains in the air for 6 seconds. Did you win the competition? YES
Situation 2:
Phil and Jenni are passing a soccer ball back and forth during recess. When Jenni kicks the soccer ball, the equation for the balls distance from the ground is y= -x² + 4x +12. When Phil kicks the ball, the equation for the ball's distance from the ground is y= -x² -x +12. The y represents the ball's distance from the ground and the x represents the amount of time it is in the air. Who kicks higher? (Hint: find the vertex)
Jenni's vertex:
-b/ 2a -4/2 (-1) -4/-2 = 2 x= 2 y= -x² + 4x +12 y= -(2)² + 4(2)+12 y= -4 + 8 +12 y = 16 Vertex : ( 2, 16) |
Phil's vertex:
-b/2a -(-1)/ 2(-1) 1/-2 x= -0.5 y= -x² -x +12 y= -(-0.5)² -(-0.5) +12 y= -(0.25) +0.5 +12 y= 12.25 Vertex: ( -0.5, 12.25) |
Answer: Jenni kicks higher than Phil.