a)
The roller coaster track resembles a parabola, so you'll need to use a quadratic equation in the form:
y = a(x - h)^2 + k
* The vertex is at (2, 12) so, h = 2 and k = 12
* The graph passes through (0, 8)
Substitute to find 'a':
8 = a(0 - 2)^2 + 12
a = -1
Equation: y = -(x - 2)^2 + 12
b)
To find the equation of the straight track, you would need the slope between (5, 8) and another point on the curve. Let's use the vertex (2, 12):
Slope (m) = (12 - 8) / (2 - 5) = -4/3
Using point-slope form with (5, 8):
y - 8 = (-4/3)(x - 5)
Equation: y = (-4/3)x + 28/3
you're welcome!
