How do you sketch a quadratic graph?

There are three things to think about when sketching a quadratic graph: whether its a 'u' or 'n' shape, where it cuts across the y axis and where it cuts across the x axis (if it does). Let's look at an example: y= -3x² +x+10A minus sign before the x² means it's a 'n' shape (like a sad face because it's negative) and if there wasn't a minus sign before the x² , it would be a 'u' shape (happy face). The graph cuts through the y axis when the x co-ordinate is 0 so substitute x with zero and we get y=10 (our y-intercept). The x co-ordinates where the graph cuts across the x axis are called the roots. The roots occur when the y co-ordinates are 0 so substitute y for 0. This leaves us with the quadratic equation -3x²+x+10=0. Solve this equation to get the roots using completing the square, the quadratic formula or factorisation. This time we can factorise: (3x+5)(-x+2)=0. Hence the roots are -5/3 or 2. Now draw the graph: it's an 'n' shape that cuts across the y axis at 10 and the x axis at -5/3 and 2.