Test 2 – Problem Solving Task
The problem
A quadratic equation was crucial in determining whether the basketball hit the hoop, thereby leading to a successful shot. Moreover, it is essential to note that higher chances of basketball successfully hitting the hoop is dependent on the height of the peak from the ground.
Plan
The plan involved measuring the height of the vertex, and the horizontal distance of the tennis ballplayer from the hoop was preferable since it was easy.
Implementation of the plan
The height of the tennis ball was 13.9 while the horizontal distance of the player from the hoop was 24.9. The center for the ball was at 0, similarly the angle of the shot was also at zero. Equation 1 was important in solving the mathematical problem.
y = a (x-n) 2 + k where
n represents x intercept of the vertex
k represents the y intercept of the vertex
y = a (x- (-1)) 2 + 4
The y intercept is (-7.5, -1)
-1= a (-7.5- (-1)) 2 + 4
-1 = a (-6.5) 2 + 4
-5 = 42.25a
-0.1183 = a
Quadratic equation for the tennis ball: y = -0.1183 (x- (-1)) 2 + 4
Interpretation of the results
The coordinate of the hoop is (4, 1)
1 = -0.1183 (4- (-1)) 2 + 4
1= 1.0425
The hoop was very close to the parabolic equation. Therefore the ball should have gone through the hoop successfully. Moreover, there was a small difference of 0.0425, allowing the ball to go through the loop. The position at which the tennis ball will fail to go through the hoop is as shown below.
0 = -0.1183 (x- (-1)) 2 + 4
-4 = -0.1183(x-(-1)) 2
=
5.8148 = x + 1
X = 6.8148
Or
X = 4.8148
Therefore the tennis ball will not go through the hoop at coordinates (6.8148, 0) or (4.8148, 0)