Question 612998
{{{y=-3x^2+x+1}}} is not a linear function. It's a quadratic function. Its graph is a parabola. Parabolas are endless curves with a smiley mouth shape (if the number in front of the {{{x^2}}} is positive), or a frowning mouth shape (if the number in front of the {{{x^2}}} is negative).
In this case, you got a frowny graph.
{{{graph(300,300,-2,2,-8,2,-3x^2+x+1)}}}
You could have asked about how to find the axis of symmetry, or the coordinates of the vertex, or even the equation of the directrix.
I do not want to give you more complication than you wanted, but I do not know what you needed.
The axis of symmetry is the line with the equation {{{x=1/6}}}, based on the coefficient of the x (1) divided by (-2) and divided by the coefficient of the {{{x^2}}}, (-3).
The y-coordinate of the vertex can be found by substituting {{{x=1/6}}} in the function, and calculating the y value.