the function models the number of accidents, ( f(x) ), per 50 million miles driven as a function of a…
the function models the number of accidents, ( f(x) ), per 50 million miles driven as a function of a drivers age, ( x ), in years, where ( x ) includes drivers from ages 16 through 68, inclusive. the graph of ( f ) is shown. use the equation for ( f ) to solve the problem below.\n\nfor what value of ( x ) does the graph reach its lowest point? use the equation for ( f ) to find the minimum value of ( y )\n\n( x=square, y=square )\n\ndescribe the practical significance of this minimum value\n\nthe minimum number of accidents is ( square ) per 50 million miles driven and is attributed to ( square )-year-old drivers
Answer
Explanation:
Step1: Find the (x) - value of the vertex
For a quadratic function (y = ax^{2}+bx + c), the (x) - coordinate of the vertex is given by (x=-\frac{b}{2a}). In the function (f(x)=0.4x^{2}-33.6x + 885.6), (a = 0.4) and (b=-33.6). [x=-\frac{-33.6}{2\times0.4}=\frac{33.6}{0.8}=42]
Step2: Find the (y) - value of the vertex
Substitute (x = 42) into the function (f(x)=0.4x^{2}-33.6x + 885.6). [ \begin{align*} f(42)&=0.4\times(42)^{2}-33.6\times42 + 885.6\ &=0.4\times1764-1411.2+885.6\ &=705.6-1411.2 + 885.6\ &=(705.6+885.6)-1411.2\ &=1591.2-1411.2\ &=180 \end{align*} ]
Answer:
(x = 42,y = 180) The minimum number of accidents is (180) per 50 million miles driven and is attributed to (42) - year - old drivers.