The equation of the parabolas given will be found as follows:
a] general form of the parabolas is:
y=k(ax^2+bx+c)
taking to points form the first graph say (2,-2) (3,2), thus
y=k(x-2)(x-3)
y=k(x^2-5x+6)
taking another point (-1,5)
5=k((-1)^2-5(-1)+6)
5=k(1+5+6)
5=12k
k=5/12
thus the equation will be:
y=5/12(x^2-5x+6)
b] Using the vertex form of the quadratic equations:
y=a(x-h)^2+k
where (h,k) is the vertex
from the graph, the vertex is hence: (-2,1)
thus the equation will be:
y=a(x+2)^2+1
taking the point say (0,3) and solving for a
3=a(0+2)^2+1
3=4a+1
a=1/2
hence the equation will be:
y=1/2(x+2)^2+1
Answer: 
Step-by-step explanation:
Given
The dimension of the box is
Space occupied by the box is equal to its volume i.e.
The volume of the box is .
The distance from Dan's house to Samuel's house is 4 km
The distance from Dan to Samuel house, Dan to Cindy house and Samuel to Cindy house forms a right angled triangle.
Distance from Dan to Samuel house = x, Distance from Dan to Cindy house = 3 km and Distance from Cindy to Samuel house = 5 km
Pythagoras theorem shows the relationship between the lengths of a right angled triangle.
Using Pythagoras theorem:
5² = x² + 3²
25 = x² + 9
x² = 16
x = 4 km
Hence the distance from Dans house to Samuel's house is 4 km
Find out more at: brainly.com/question/21846482
Answer:
x = 12
Step-by-step explanation:
9*x-4*(x-3)-(72)=0
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(9x - 4 • (x - 3)) - 72 = 0
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
5x - 60 = 5 • (x - 12)
