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)

The equation of M is

Step-by-step 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

---->

---->

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

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