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) Depth of Person from Surface of Water, d(x) (feet)
1 negative 1.8 5
−1.85
4 negative 7.2 8
−7.28
6 negative 8.3
−8.3
8.5 negative 6.6 5
−6.65
10 negative 4.1
−4.1
11.5 negative 0.3 8
−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
To determine which function best models the data, we need to find a quadratic function that fits the given data points. We can plug the values of x and d(x) into each answer choice and see which one gives us the closest values.
Using the data points:
(1, -1.85), (4, -7.28), (6, -8.3), (8.5, -6.65), (10, -4.1), (11.5, -0.38)
a) d(x) = 0.05x^2 + 0.74x
- Plug in x = 1: d(1) = 0.05(1)^2 + 0.74(1) = 0.79
- This value does not match the given depth of -1.85
b) d(x) = 0.05x^2 + 0.74x + 9.17
- Not the correct answer since the other choices do not match the given depth values
c) d(x) = 0.26x^2 - 3.11x
- Plug in x = 1: d(1) = 0.26(1)^2 - 3.11(1) = -2.85
- This value is slightly closer to the given depth of -1.85
d) d(x) = 0.26x^2 - 3.11x + 1
- Not the correct answer since the other choices do not match the given depth values
The function that best models the data is choice c: d(x) = 0.26x^2 - 3.11x