Answer:
Step-by-step explanation:
The parabola is passing through (0,24)
a)
[tex]y=(4-x)(x+k)\\\\24=4*k\\k=\dfrac{24}{4} \\k=6\\[/tex]
b)
coordinates of B and C
y=0 ==> (4-x)(x+6)=0 ==> x= -6 or x=4
B=(-6,0)
C=(4,0) since C is on the right of B.
c)
Maximum of the curve:
y=(4-x)(x+6)=-x²-2x+24
y'=-2x-2=0 ==> x=-1 and y=5*5=25
Max =25
d)
D=(1,m) ==> m=(4-1)*(1+6)=3*7=21
O=(0,0)
slope of OD =(m-0)/(1-0)=21
Equation of OD: y-0=(x-0)*21 ==> y=21 x
e)
y=9 ==> -x²-2x+24=9 ==> x=3 or x=-5
P=(-5;9 )
Q=(3;9) since Q is on the right of P
