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:
5x-5
Step-by-step explanation:
X = -1/2 (negative)
y = - 1.8 (negative)
so It's in Quadrant 3
Answer:
Length is 14
Width is 6
Step-by-step explanation:
Length = 2W + 2
Width = W
Perimeter is twice the length + twice the width
P = 40 = 2(2W+2) + 2W first simplify
40 = 4W + 4 + 2W now combine terms
40 = 6W + 4 and subtract 4 from both sides
36 = 6W
Width W = 6
Length = 2W + 2 = 12 + 2 = 14
Given:
The function is
The binomial 
is a factor of f(x).
To find:
The value of 
.
Solution:
If 
is a factor of f(x), then 
.
It is given that, is a factor of f(x), then 
.
We have,
Substituting x=4, we get
Now,
Therefore, the value of a is 5.
