Answer:
Equation for M → g(x) = [tex]\frac{5}{4}x^{2} + 2[/tex]
Equation for N → h(x) = [tex]\frac{5}{4}(x+4)^2-1[/tex]
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 = [tex]\frac{5}{4}[/tex]
Hence, we get the equation of the function 'f' as,
f(x) = [tex]\frac{5}{4}x^{2} -1[/tex]
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) = [tex]\frac{5}{4}x^{2} - 1 + 3[/tex]
g(x) = [tex]\frac{5}{4}x^{2} + 2[/tex]
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) = [tex]\frac{5}{4}(x+4)^2-1[/tex]
