What is the closest point of the parabola y = 7x^2 + 9x + 3 to the x-axis?

Without using calculus, we know that the vertex is the
maximum or minimum of the parabola.  We can use the formula for the x
position of the vertex.

In this case a = 7, b =
9

This gives us the x coordinate of the
vertex.

(-b)/(2a)=(-9)/(2(7))=-9/14

Now the y coordinate when
we evaluate at

We
get

7(81/196)+9(-9/14)+3=81/28-81/14+3

GCD =
28

So
the closest gets to the x axis is

3/28)