Answer:
[tex]f(x)=\frac{3}{5}(x+1)^2+4[/tex]
Step-by-step explanation:
The equation of a quadratic function in vertex form is given by:
[tex]f(x)=a(x-h)^2+k[/tex]
Where (h,k) is the vertex.
It was given in the question that the vertex of the parabola is (-1,4).
When we substitute the vertex into the formula we get:
[tex]f(x)=a(x+1)^2+4[/tex]
The parabola also passes through (4,19) hence it must satisfy its equation.
[tex]19=a(4+1)^2+4[/tex]
[tex]19-4=a(5)^2[/tex]
[tex]15=25a[/tex]
We divide both sides by 25 to get:
[tex]a=\frac{15}{25}= \frac{3}{5}[/tex]
Hence the quadratic function is:
[tex]f(x)=\frac{3}{5}(x+1)^2+4[/tex]
