Question

If the parabolas given by `y=2x^2+6x+5` and `y=x^2+a` are tangent, what is the abscissa of the tangency point?

Answer 1

They are tangent at `x = -3` for `a = -4`

Explanation:

Given the two parabolas
`p_1->y=2x^2+6x+5` ans
`p_2->y = x^2+a`
If they are tangents then they must have a common point.
Solving `2x^2+6x+5=x^2+a` for `x` we can find their common points. The result gives us two points
`x -> -3 - sqrt(4 + a), x -> -3 + sqrt(4 + a)`
Choosing `a = -4` we will have only one common point which is for
`x = -3`