We know that the points at which the parabola intersects the x axis are
(-5,0) and (1,0)
So the extent between these two points would be the base of the triangle
lets find the length of the base using the distance formula
![\sqrt{[(-5-1)^{2}+(0-0)^{2} ]}](https://tex.z-dn.net/?f=%20%5Csqrt%7B%5B%28-5-1%29%5E%7B2%7D%2B%280-0%29%5E%7B2%7D%20%5D%7D%20%20)
the base b=6
We will get the height of the triangle when we put x=0 in the equation
y=a(0+5)(0-1)
y=-5a
so height = -5a (we take +5a since it is the height)
We know that the area of the triangle =
× 6 × (5a) = 12
15a=12
a= 
See picture for reply and solution steps.
Easy peasy
the average rate of change in section A is the slope from (1,g(1)) to (2,g(2))
the average rate of chagne in section B is the slope from (3,g(3)) to (4,g(4))
A.
section A
g(1)=4(3)^1=12
g(2)=4(3)^2=4(9)=36
slope=(36-12)/(2-1)=24/1=24
section B
g(3)=4(3)^3=4(27)=108
g(4)=4(3)^4=4(81)=324
slope=(324-108)/(4-3)=216/1=216
section A has an average rate of change of 24
section B has an average rate of change of 216
Answer:
12a^6b^3 you multiply 4 and 3 to get 12,then you factor out the algebra with the common terms.