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 `x=(-b)/(2a)` for the x
position of the vertex.

In this case a = 7, b =
9

This gives us the x coordinate of the
vertex.

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

Now the y coordinate when
`x=-9/14` we evaluate `y=7x^2+9x+3` at `x=-9/14`

We
get

`y = 7(-9/14)^2 + 9(-9/14) + 3 =
7(81/196)+9(-9/14)+3=81/28-81/14+3 `

GCD =
28

`81/28-162/28+84/28=3/28`

So
the closest `7x^2+9x+3` gets to the x axis is

`(-9/14,
3/28) ` Same answer as above but without Calculus.