According to the vertex and the directrix of the given parabola, the equation is:
[tex]y = \frac{3}{4}(x - 1)^2 + 4[/tex]
The equation of a quadratic function, of vertex (h,k), is given by:
[tex]y = a(x - h)^2 + k[/tex]
In which a is the leading coefficient.
The directrix is at y = k + 4a.
In this problem, the vertex is (1,4), hence:
[tex]h = 1, k = 4[/tex]
The directrix is at y = 7, hence:
[tex]4 + 4a = 7[/tex]
[tex]a = \frac{3}{4}[/tex]
Hence, the equation is:
[tex]y = a(x - h)^2 + k[/tex]
[tex]y = \frac{3}{4}(x - 1)^2 + 4[/tex]
More can be learned about the equation of a parabola at https://brainly.com/question/26144898