Find the coordinates of the turning point of the graph y=x^2 -x -12. Use it to sketch the graph on a set of x-y axis.

-Firstly we should check if the equation has the variables separated (x on one side and y on the other side of the equal sign), which they apear to are, therefore we can proceed to the next step. As it is known, at a curve's turning point, the gradient is zero, which in more of a mathematical sense, it means that the derivative of the curve will be equal to zero. When differentiating the curve (by bringing the power of x down and then subtracting 1 from the actual power -> easily explained when I am writing it down), we get dy/dx = 2x-1 and then we set that equal to zero. By solving the nwe equation we find that x= 0.5 which when we put in the initial equation we get that the y value for that x is -12.25. Therefore the turning point is ( 1/2 , -12.25).-When trying to plot, the turning point will have a zero gradient, and when drawing the quadratic graph, since the coefficient of x is positive, the graph will look like a smile curve (like a U). It might be useful in an exam to label the axis of symmetry of the curve, which will pass through the line x = 1/2 and the places the curve cuts the axis when each of the two variables are zero (At (0,-12) and (-3,0) and (4,0) which can be found by factorising the above curve equation when y=0)