Answer: C= (3,2) and D=(2.2, 2.8)
Step-by-step explanation:
The coordinates of point P(x,y) divides a line segment having end points M and N
in m:n will be :-
Given : The endpoints of AB are A(1,4) and B(6,-1).
If point C divides AB in the ratio 2 : 3, the coordinates of point C will be :-
Simplify,
Thus , coordinate of C= (3,2)
If point D divides AC in the ratio 3 : 2, the coordinates of point D will be :-
Simplify,
Thus , coordinate of D= (2.2,2.8)
Answer:
Step-by-step explanation:
A. y-Intercept of ƒ(x)
ƒ(x) = x² - 4x + 3
f(0) = 0² - 4(0) + 3 = 0 – 0 + 3 = 3
The y-intercept of ƒ(x) is (0, 3).
If g(x) opens downwards and has a maximum at y = 3, it's y-intercept is less than (0, 3).
Statement A is TRUE.
B. y-Intercept of g(x)
Statement B is FALSE.
C. Minimum of ƒ(x)
ƒ(x) = x² - 4x + 3
a = 1; b = -4; c = 3
The vertex form of a parabola is
y = a(x - h)² + k
where (h, k) is the vertex of the parabola.
h = -b/(2a) and k = f(h)
h = -b/2a = -(-4)/(2×1 = 2
k = f(2) = 2² - 4×2 + 3 =4 – 8 +3 = -1
The minimum of ƒ(x) is -1. The minimum of ƒ(x) is at (2, -1).
Statement C is FALSE.
D. Minimum of g(x)
g(x) is a downward-opening parabola. It has no minimum.
Statement D is FALSE