1. Bill bikes 4km to school. After 5 min he is 3.2 km from the school:

-a.Give an equation of the linear function.
-b.Use the equation to find approximately how long it takes Bill to bicycle to school.


Find an equation of the quadratic function described:

2. Its graph is a parabola with x-intercepts 2 and -1 and y-intercept 6
3. The function "f" has zeros 5 and 1 and f(0) = 1




if you guys could help me out a little, that'd be awesome. i forgot so much over the summer lol

1a. slope = 0.8 km / (1/12 hour) = 9.6 km/hr

so let distance = d:
d = (9.6 km/hr) * t

1b. set d = 4 km:
(9.6 km/hr) * t = 4 km
t = 0.41666.. hours, or 25 minutes.

2. y = ax^2 + bx + c

Use the intercepts to define 3 equations:
0 = a(2)^2 + b(2) + c
0 = a(-1)^2 + b(-1) + c
6 = a(0)^2 + b(0) + c

Now solve for a, b, and c:
c = 6
0 = 4a + 2b + 6 => 2a = -(b + 3) => a = -(b + 3)/2
0 = a - b + 6 => 0 = -(b+3)/2 - b + 6 => -3/2 (b + 1) = -6 => b + 1 = 4 => b = 3

0 = 4a + 3*2 + 6 => 4a = -12 => a = -3

So the equation is:
y = -3x^2 + 3x + 6


3. f(x) = ax^2 + bx + c

0 = a(5)^2 + b(5) + c
0 = a(1)^2 + b(1) + c
1 = a(0)^2 + b(0) + c


=> c = 1
=> 0 = a(1)^2 + b(1) + 1 => a + b = -1 => a = -(b + 1)
0 = a(5)^2 + b(5) + 1 => 0 = -25(b+1) + 5b + 1 => 0 = -20b - 24 => b = -24/20 => b = -1.2
0 = a + (-1.2) + 1 => a = 0.2

So in total:
f(x) = 0.2x^2 - 1.2x + 1

This post was edited by neal448 on Aug 31 2010 08:23pm