Given three points
P1(-2,8)
P2(0,-4)
P3(4,68)
We need the quadratic equation that passes through all three points.
Solution:
We first assume the final equation to be
f(x)=ax^2+bx+c .............................(0)
Observations:
1. Points are not symmetric, so cannot find vertex visually.
2. Using the point (0,-4) we substitute x=0 into f(x) to get
f(0)=0+0+c=-4, hence c=-4.
3. We will use the two other points (P1 & P3) to set up a system of two equations to find a and b.
f(-2)=a(-2)^2+b(-2)-4=8 => 4a-2b-4=8.................(1)
f(4)=a(4^2)+b(4)-4=68 => 16a+4b-4=68.............(2)
4. Solve system
2(1)+(2) => 24a+0b-12=84 => 24a=96 => a=96/24 => a=4 ......(3)
substitute (3) in (2) => 16(4)+4b-4=68 => b=8/4 => b=2 ..........(4)
5. Put values c=-4, a=4, b=2 into equation (0) to get
f(x)=4x^2+2x-4
Check:
f(-2)=4((-2)^2)+2(-2)-4=16-4-4=8
f(0)=0+0-4 = -4
f(4)=4(4^2)+2(4)-4=64+8-4=68
So all consistent, => solution ok.
When you have a power to a fraction, you simply take it by the top and then by the bottm.
So, split it into two: (2)^4 and (5)^4
Solve: (2)^4=16
(5)^4=625
So the fraction is: 16/625
Check to see if it reduces: It doesn't. (Odd and even numbers that have no common multiples).
Therefore, that's the answer.
X=-12,-5/2 you could find the answer by solving for x
For this case the distance will be given by:
d ^ 2 = (12 * 1.5) ^ 2 + (8 * 1.5) ^ 2
Rewriting we have:
d ^ 2 = (18) ^ 2 + (12) ^ 2
d ^ 2 = 324 + 144
d ^ 2 = 468
d = root (468)
d = 21.63 Km
Answer:
1) She did not find the full distance each traveled in 1.5 hours.
2) She should have used 12 km for Joseph's distance and 18 km for Isabelle's distance.
