Adrianne is playing soccer, and kicks the ball at the goal. The ball follows the path of a quadratic function. When she kicks the ball, she is 20 feet away from the goal, and the ball hits a maximum height of 10 feet when it is 5 feet away from the goal line. If the net is 8 feet tall, does she make a goal (assuming the goalie does not stop the ball)? a. Draw a diagram of the situation, including known values.
7 years ago
Answered By Jules T
For she to make a goal, the ball must reach the net (20,8) at less than 8 feet height (y<8)
The ball follows the path of a quadratic function: y=ax2+bx+c (1)
The ball is at the origin à c=0
The function reaches its maximum at the vertex point (15,10) Note: On x-axis, the vertex is located at 5ft from the goal line and 15ft from the ball (The goal line is 20ft from the ball)
y=a(x-15)2+10 = ax2-30ax+225a+10 (2)
Comparing (1) and (2) à b=-30a and c=225a+10 =0 à a=-2/45 à y=-2/45(x-15)2+10
At x=20 (goal line), y=80/9 > 8 ft. The ball is above the net à No goal scored
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