How do you find the axe of symetry, summit, and minimum/maximum from two points on a parabola? Example, the points (5,-2) and (-9,-2) are on a parabola. What is the summit? How do you find it?
you can't find all that information with just two points ... unless you know the value of the leading coefficient for the parabola's equation.
you can find the axis of symmetry ... since (5,-2) and (-9,-2) have the same y-value, the axis of symmetry will split the x-values. the equation for the axis of symmetry is ...
$\displaystyle x = \frac{-9+5}{2} = -2
$
I will guess that, by "summit", you mean "vertex". However, without more information, I'm afraid there is no way to find "the" quadratic through the two points.
The x-value of the vertex will be exactly midway between the x-value of the two listed points, since their y-values are the same. But there is no way to be sure of the y-value of the vertex, or if the vertex is a maximum or a minimum. Sorry.
You can only find the axis of symmetry, as stated.
As an example, try graphing $\displaystyle y = x^2 - 9$ and $\displaystyle y = \frac{1}{2}x^2 - 4$ on the same set of axes. At y = 1, you'll notice that the points $\displaystyle (-2\sqrt{2},1)$ and $\displaystyle (2\sqrt{2},1)$ belong to both graphs.