Write the standard form of the equation of the parabola that has the indicated vertex and whose graph passes through the given point. show all work. vertex(4,7)point(3,6)

Vertex form of parabola is

y = a(x - b)^2 + c   where a is a constant and  the vertex is at the point (b,c)

so here we have

y = a(x - 4)^2 + 7

To find value of a we plug in the point  (3,6)

6 = a(3 - 4)^2 + 7
6 = a + 7
a =  6-7 = -1

so equation is y = -(x - 4)^2 + 7

Covert to standard form:-
y = -(x^2 - 8x + 16) + 7
y = -x^2 + 8x - 9