Question

The graph of a quadratic function has a vertex at `(2,0)`. one point on graph is `(5,9)` How do you find the other point? Explain how?

Answer 1

Another point on the parabola that is the graph of the quadratic function is `(-1, 9)`

Explanation:

We are told that this is a quadratic function.

The simplest understanding of that is that it can be described by an equation in the form:

`y = ax^2+bx+c`

and has a graph that is a parabola with vertical axis.

We are told that the vertex is at `(2, 0)`.

Hence the axis is given by the vertical line `x=2` which runs through the vertex.

The parabola is bilaterally symmetric about this axis, so the mirror image of the point `(5, 9)` is also on the parabola.

This mirror image has the same `y` coordinate `9` and `x` coordinate given by:

`x = 2 - (5 - 2) = -1`

So the point is `(-1, 9)`

graph{(y-(x-2)^2)((x-2)^2+y^2-0.02)(x-2)((x-5)^2+(y-9)^2-0.02)((x+1)^2+(y-9)^2-0.02) = 0 [-7.114, 8.686, -2, 11]}