Question

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)

Answer 1

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