To predict the stopping distance when traveling at 80 miles per hour using the given quadratic regression equation [tex]\( y = 0.06x^2 + 0.31x + 4 \)[/tex]:
1. Identify the coefficients for the quadratic regression equation:
- [tex]\( a = 0.06 \)[/tex]
- [tex]\( b = 0.31 \)[/tex]
- [tex]\( c = 4 \)[/tex]
2. Substitute [tex]\( x = 80 \)[/tex] into the equation, where [tex]\( x \)[/tex] is the speed in miles per hour.
3. Calculate each term individually:
[tex]\[
0.06 \cdot (80)^2 = 0.06 \cdot 6400 = 384.0
\][/tex]
[tex]\[
0.31 \cdot 80 = 24.8
\][/tex]
[tex]\[
4 \text{ (constant term)}
\][/tex]
4. Add the results of these calculations together to get the stopping distance:
[tex]\[
384.0 + 24.8 + 4 = 412.8
\][/tex]
Therefore, the stopping distance when traveling at 80 miles per hour, using the equation provided, is:
[tex]\[
\boxed{412.8 \text{ ft}}
\][/tex]
Among the options provided, the correct answer is b. [tex]\( 412.8 \text{ ft} \)[/tex].
