The graph of y=f(x) is shown on the grid
​

Equation for M → g(x) =

Equation for N → h(x) =

Step-by-step explanation:

Vertex of the graph of y = f(x) is (2, -1)

Therefore, equation of the function will be,

y = a(x - 2)² - 1

Since this graph passes through a point (0, 4),

4 = a(0 - 2)² - 1

4 = 4a - 1

a =

Hence, we get the equation of the function 'f' as,

f(x) =

Now this graph has been shifted 3 unit up to get the new graph M

Equation for M will be,

g(x) = f(x) + 3

g(x) =

g(x) =

Further graph of function 'f' is shifted 4 units to the left then equation of the new function (N) will be,

h(x) = f(x + 4)

h(x) =

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step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.