To determine which function best models the data, we can create a system of equations using the data provided.
When x = 1:
d(1) = -1.85
Plugging into the quadratic function,
-1.85 = 0.05(1)^2 + 0.74(1) + C
-1.85 = 0.05 + 0.74 + C
C = -1.85 - 0.05 - 0.74
C = -2.64
When x = 4:
d(4) = -7.28
Plugging into the quadratic function,
-7.28 = 0.05(4)^2 + 0.74(4) - 2.64
-7.28 = 0.05(16) + 2.96 - 2.64
-7.28 = 0.8 + 0.32
-7.28 = 0.32
This shows that the function d(x) = 0.05x^2 + 0.74x - 2.64 does not fit the data points.
Similarly, when x = 6, 8.5, 10, and 11.5, the function d(x) = 0.05x^2 + 0.74x - 2.64 does not give the correct values for depth.
Therefore, the function d(x) = 0.26x^2 - 3.11x + 1 seems to be the best model for the data points provided.
A person dives into a pool from its edge to swim to the other side. The table shows the depth in feet of the person from the surface of the water after `x` seconds. The data can be modeled by a quadratic function.
Which function best models the data?
Time, x (seconds):1,4,6,8.5,10,11.5
Depth of Person from Surface of Water, d(x) (feet):−1.85,−7.28, −8.3, −6.65, −4.1, −0.38
Answer choices:
d\left(x\right)=0.05x^{2}+0.74x
d\left(x\right)=0.05x^{2}+0.74x+9.17
d\left(x\right)=0.26x^{2}-3.11x
d\left(x\right)=0.26x^{2}-3.11x+1
1 answer