We first identify that a = -1, b = 1 and c = 6

Step (a) Since a = -1, a < 0 hence the function is a parabola with a maximum point and it opens downwards (n-shaped)

Step (b) The x co-ordinate of the maximum point is

So

Step (c) The y-intercept is the point (0, c) = (0, 6)

Sometimes, we need some more points to get a better sketch of the parabola.

Two points we can also find are the x-intercepts ie. points where the function cuts the x axis (where y = 0).

To find the x intercepts, we let y = 0

we get -x² + x + 6 = 0

or x² - x - 6 = 0

Factorising (x - 3) (x + 2) = 0

Solving x - 3 = 0 or x + 2 = 0

x = 3 or x = -2

Hence, the x intercepts are (3, 0) and (-2, 0)