Question

Coordinate geometry

Answer 1

Explanation:

The parabola is passing through (0,24)

a)

`y=(4-x)(x+k)\\\\24=4*k\\k=(24)/(4) \\k=6\\`

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