Question

What is the axis of symmetry and vertex for the graph `f(x) = 3 + 2x – x^2`?

Answer 1

axis of symmetry is `x = 1`
Vertex is at `(1,4)`

Explanation:

This is an example of a parabola. It has the standard form:
`f(x) = y = ax^2 + bx + c`
In `f(x) = -x^2 + 2x + 3" "` a = -1, b = 2, c = 3.

The formula to find the axis of symmetry is: `x = (-b)/(2a)`

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

The vertex lies on the axis of symmetry, if `x = 1`

`y = -(1) + 2(1) + 3 = 4`

Vertex is at (1,4)