Answer :

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!