i'm pretty sure it's true :
Thought you'd want to know: If you're talking about parabolas, it's parabolas, not probables. ;)
The standard equation of a a quadratic is y = ax^2 + bx + c. We need to find the values of the coefficients a, b and c.
Taking the first point: When x=3, y=0, so write 0 = a(3)^2 + b(3) + c, or
0 = 9a + 3b + 1c
Do the same for points (-2,3) and (-1,4).
You will have obtained three linear equations in a, b and c:
3= a(-2)^2 + b(-2) + c, or 3 = 4a - 2b + 1c, also
4 = a(-1)^2 + b(-1) + 1c, or 1a - 1b + 1c.
I used matrix operations to solve this system. The results are:
a= -2/5, b= 1/5, c= 21/5
and so the function f(x) is f(x) = (-2/5)x^2 + (1/5)x + 21/5.
The number representing Liam's share is 2; for Sarah's share, it is 3. The difference of those is 1, so each 1 unit of share must be £30, the difference between the amount Sarah got and the amount Liam got.
Emily got 5 shares or £30 × 5 = £150.
Answer:
The answers are:
a) 
is FALSE.
b) 
is TRUE.
c) 
is FALSE.
d) 
is FALSE.
e) 
is FALSE.
f) 
is TRUE.
g) 
is FALSE.
h) 
is FALSE.
Step-by-step explanation:
We can show that the FALSE statement are, in fact, false finding an example where the equality fails.
a) Take x=2 and y=3 and notice that (2+3)² = 25, while 2²+3²=4+9=13.
b) (x+y)² = (x+y)(x+y)=x²+xy+xy+y² = x² +2xy +y².
c) Take x=2 and y=3 and notice that 2/(2+3) = 2/5 which is different from 1/3.
d) Take x=2 and y=3 and notice that 2-(2+3) = 2-5=-3 which is different from 3. Recall that x-(x+y) = x-x-y=-y.
e) Take x=-2, and notice that [tax]\sqrt{(-2)^2} = \sqrt{4} = 2[/tex] which is different from -2.
f) The previous example illustrate why this is true.
g) Take x=1, and notice that 
which is different from 3.
h) Take x=2 and y=3 and notice that 1/(2+3)=1/5 and 1/3+1/2 = 5/6.
