Iadratic Formula
Question 1,8.2.77
HW Score: $25\mathrm{\%},0.5$ of 2 points
Points: 0 of 1

A driver has something to do with his or her chance of getting into a fatal car crash. The bar graph shows the number of fatal vehicle crashes per 100 million miles driven for drivers of various age groups. For example, 25 -year-old drivers are involved in 4.1 fatal crashes per 100 million miles driven. Thus, when a group of 25 -year-old Americans have driven a total of 100 million miles, approximately 4 have been in accidents in which someone died. The number of fatal vehicle crashes per 100 million miles, $f(x)$, for drivers of age $x$ can be modeled by the following quadratic function.
$$f(x)=0.013x^2-1.19x+28.24$$

What age groups are expected to be involved in 2 fatal crashes per 100 mill miles driven?
-year-olds
(Round to nearest whole number. Use a comma to separate answers as nee

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Step 1 ：The question is asking for the age groups that are expected to be involved in 2 fatal crashes per 100 million miles driven. This means we need to solve the equation $f(x)=2$ for $x$, where $f(x)$ is the quadratic function given in the problem.

Step 2 ：We can solve this equation using the quadratic formula. The quadratic formula is given by $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$, where $a$, $b$, and $c$ are the coefficients of the quadratic equation $a{x}^2+bx+c=0$.

Step 3 ：In this case, $a=0.013$, $b=-1.19$, and $c=28.24-2=26.24$. We can plug these values into the quadratic formula to find the solutions for $x$.

Step 4 ：The solutions for $x$, which represent the ages at which the number of fatal vehicle crashes per 100 million miles driven is expected to be 2, are approximately 54.51 and 37.03.

Step 5 ：However, the question asks for the ages to be rounded to the nearest whole number. Therefore, we need to round these solutions to the nearest whole number.

Step 6 ：The age groups that are expected to be involved in 2 fatal crashes per 100 million miles driven are $\boxed{{\displaystyle 55}}$ and $\boxed{{\displaystyle 37}}$ year-olds.