How do I skecth a grpah of y = x^2 - 7x + 10?

To plot any graph, you usually only need to find a few points that are on that graph to the sketch it. With a quadratic like this, the easiest way to do this is to find where the graph crosses the x and y axis'. To find where is crosses the y-axis all that you need to do is plug x=0 into your equation - where in this case you'd get y=10. So, you know that the graph crosses the y-axis at 10 and so you can plot this point. To find where it crosses the x-axis you will need to plus y=0 into your equation so that you get x^2 - 7x +10 = 0. You then need to find x, and to do this you first must factorise the quadratic (you can either just look at the equation to find two numbers that add up to -7 AND multiply to 10, or you may use the quadratic equation). This should then give you (x-2)(x-5)=0. From this we can see that either x-2=0 or x-5=0, therefore the two possible values of x when y=0 (i.e. on the x-axis) are 2 and 5. These points can also be plotted. At this point, it should be clear how to draw a smooth curve between these points!