56.6666... to the nearest tenth is <u>57</u>.
Answer:
A and A
the equation of a parabola in vertex form is
y = a(x - h)² + k
where ( h, k ) are the coordinates of the vertex and a is a multiplier
y = - 2(x + 3)² + 2 is in this form
with vertex = ( - 3, 2)
To find the y-intercept let x = 0
y = - 2(3)² + 2 = - 18 + 2 = - 16
Similarly
y = - 2(x + 2)² + 2 is in vertex form
vertex = ( - 2 , 2)
x = 0 : y = - 2(2)² + 2 = - 8 + 2 = - 6 ← y- intercept
hope this helped
There you go I hope it helps
Answer:
Maximum height is 7 feet
Step-by-step explanation:
Solution:-
- The complete question is as follows:
" The height of a small rise in a roller coaster track is modeled by f(x) = –0.07x^2 + 0.42x + 6.37, where x is the distance in feet from a supported at ground level.
Find the greatest height of the rise "
- To find any turning points ( minimum or maximum ) points of a trajectory expressed as function of independent parameter, we find the critical points of the trajectory where the first derivative of the dependent variable w.rt independent variable is set to zero.
- In our case the height of the roller coaster track (y) is function of the distance (x) from a supported pole at ground level.
f(x) = –0.07x^2 + 0.42x + 6.37
- Now set the first derivative equal to zero, and determine the critical values of x:
0 = -0.14x + 0.42
x = 0.42 / 0.14 = 3 ft
- The critical value for the coaster track is at point 3 feet away from the supported pole at ground level. So the height f(x) at x = 3 ft, would be:
f ( x = 3 ) = max height
max height = –0.07*3^2 + 0.42*3 + 6.37
= 7 ft
