Question

M(4,2)

N(-1,-2)
The figure shows two quadratic graphs M and N. N is a translation of M such that
the point (-1,-2) on M is translated to the point (4,2) on N. The equation
of N is y=-(x - 2)2 +6.
(a) Find the equation of M.
(2 marks)​

Answer 1

The equation of M is
`y=-(x+3)^2+6`

Explanation:

we have that

The translation of M to N is

(-1,2) ----> (4,2)

The rule of the translation M to N is

(-1,2) ----> (x+a,y+b)

(-1,2) ----> (-1+a,2+b)

so

`-1+a=4` ---->
`a=4+1=5`

`2+b=2` ---->
`b=0`

The rule of the translation M to N is

(x,y) ----> (x+5,y)

The translation is 5 units right

I can say that the rule of the translation N to M is

(x,y) ----> (x-5,y)

we have the equation of N

`y=-(x-2)^2+6`

Is a quadratic equation open downward

The vertex is (2,6)

Find the vertex of M

Applying the rule of the translation N to M to the vertex

(2,6) ----> (2-5,6)

(2,6) ----> (-3,6)

therefore

The equation of M is

`y=-(x+3)^2+6`