At what point on the curve y = 3x^2 + 3x +7 is the tangent drawn perpendicular to the y axis.

The tangent drawn is perpendicular to the y
axis when it is parallel to x axis. That means that the tangent line passes through the
vertex of the function  y = 3x^2 + 3x
+7.

We'll calculate the vertex of the
parabola, using the coordinates xV and yV.

xV =
-b/2a

yV = -delta/4a

We'll
identify the coefficients a,b,c.

a =
3

b = 3

c =
7

We'll substitute the coefficients into the coordinates of
the vertex:

xV =
-3/2*3

xV =
-1/2

yV = (4ac -
b^2)/2a

yV = (84 - 9)/6

yV =
75/6

yV =
25/2

The perpendicular line to
y-axis is passing through the vertex of the parabola: V(-1/2 ,
25/2).