Question

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

Answer 1

Answer:

Equation for M → g(x) = $\frac{5}{4}x^{2} + 2$

Equation for N → h(x) = $\frac{5}{4}(x+4)^2-1$

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 = $\frac{5}{4}$

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

f(x) = $\frac{5}{4}x^{2} -1$

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) = $\frac{5}{4}x^{2} - 1 + 3$

g(x) = $\frac{5}{4}x^{2} + 2$

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) = $\frac{5}{4}(x+4)^2-1$