The general expression for the quadratic function is :
[tex]f(x)=a(x-h)^2+k[/tex]where, Vertex : (h, k) and h = -b/2a and k = f(h)
In the given question the vertex is ( -1, 3)
Substitute the value of the h = -1 and k = 3
Thus :
[tex]\begin{gathered} f(x)=a(x-h)^2+k \\ f(x)=a(x-(-1))^2+3 \\ f(x)=a(x+1)^2+3 \\ as\text{ the curve passed through : (2, 4) } \\ substitute\text{ x = 2 and at f(2) = 4} \\ f(2)=a(2+1)^2+3 \\ 4=a(3)^2+3 \\ 4=9a+3 \\ 9a=4-3 \\ 9a=1 \\ a=\frac{1}{9} \\ \text{Substitute the value in the expression :} \\ f(x)=\frac{1}{9}(x+1)^2+3 \end{gathered}[/tex]The expression for the quadratic expression is :
f(x) = 1/9(x + 1)² + 3
Answer : f(x) = 1/9(x + 1)² + 3
