SOLUTION: A roller coaster drop creates a parabolic shape while going underground. The distance from the ground in feet can be modeled by the equation y = 3x² − 24x + 36, where x is the

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: A roller coaster drop creates a parabolic shape while going underground. The distance from the ground in feet can be modeled by the equation y = 3x² − 24x + 36, where x is the      Log On


   

Question 1205935: A roller coaster drop creates a parabolic shape while going
underground. The distance from the ground in feet can be
modeled by the equation y = 3x² − 24x + 36, where x is the
number of seconds on the ride. Which of the following can
represent the domain when the roller coaster is underground?
Ⓐ x > 4
Ⓑ x < 36
Ⓒ 2 < x < 6
Ⓓ x is all real numbers.
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: 2 < x < 6

Explanation

The equation y+=+3x%5E2+-+24x+%2B+36 is of the template y+=+ax%5E2+%2B+bx+%2B+c
a = 3
b = -24
c = 36
Plug those values into the quadratic formula below.
x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

x+=+%28-%28-24%29%2B-sqrt%28%28-24%29%5E2-4%283%29%2836%29%29%29%2F%282%283%29%29

x+=+%2824%2B-sqrt%28576+-+432%29%29%2F%286%29

x+=+%2824%2B-sqrt%28144%29%29%2F%286%29

x+=+%2824%2B-++12%29%2F%286%29

x+=+%2824%2B12%29%2F%286%29 or x+=+%2824-12%29%2F%286%29

x+=+%2836%29%2F%286%29 or x+=+%2812%29%2F%286%29

x+=+6 or x+=+2

x+=+2 or x+=+6

If either x = 2 or x = 6, then f(x) = 0.

If 2 < x < 6 then the parabola is below the x axis as demonstrated by this graph.
graph%28400%2C400%2C-2%2C8%2C-15%2C20%2C-100%2C3x%5E2-24x%2B36%29
Desmos is a graphing tool I recommend.
GeoGebra is also very useful as well.