according to data from the national safety council, the fatal-accident rate per 100,000 licensed drivers can be approximated by the function
f(x)=.0328x^2 - 3.55x + 115, where x is the age of the driver (16< or equal to x < or equal to 88). at what age is the rate the lowest?
It would occur at at the vertex of this parabola
for f(x) = ax^2 + bx + c, the
x of the vertex is -b/(2a)
so x = 3.55/(2(.0328)) = appr. 54
or, if you are learning how to complete the square ...
f(x)=.0328x^2 - 3.55x + 115
= .0328(x^2 - 108.232 + 2928.53 - 2928.53) + 115
= .0328(x-54.12)^2 + 18.94
vertex is (54.12, 18.94)
etc.
thank you!
To find the age at which the fatal-accident rate is the lowest, we need to find the minimum point of the quadratic function f(x) = 0.0328x^2 - 3.55x + 115.
The formula for finding the x-coordinate of the vertex of a quadratic function in the form f(x) = ax^2 + bx + c is given by x = -b / (2a).
In this case, a = 0.0328 and b = -3.55. Plugging these values into the formula, we get:
x = -(-3.55) / (2*0.0328)
x = 3.55 / 0.0656
x ≈ 54.02
Therefore, the rate is lowest at an approximate age of 54 years old.
To find the age at which the fatal-accident rate is the lowest, we need to find the minimum value of the function f(x) = 0.0328x^2 - 3.55x + 115.
To find the minimum of a quadratic function in the form ax^2 + bx + c, we can use the formula x = -b / 2a. In our case, a is 0.0328, b is -3.55, and c is 115.
Given the formula, we substitute the values into the formula:
x = -(-3.55) / (2 * 0.0328)
x = 3.55 / 0.0656
x ≈ 54.08
Therefore, the rate is the lowest approximately at the age of 54.