Sketch the curve y=x^2-x-6

This curve is a quadratic due to the highest power in the equation being two. Quadratics typically have the shape of a U. Due to the coefficient of the x^2 term being positive, the curve is increasing for larger values of x. To find where the curve crosses the x-axis we equate the equation to zero and factorise. This results in (x-3)(x+2)=0 so the curve crosses the x-axis at either 3 or -2. This is because for the equation to be true, either x-3=0 or x+2=0. The graph crosses the y-axis when x=0, therefore at -6. The minimum of the graph can be found by completing the square. Hence y=(x-1/2)^2-25/4 and so the minimum occurs at (1/2,-25/4).